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A BUDGET OF PARADOXES 



BY 



AUGUSTUS DE MORGAN, 

F.R.A.S. AND C.P.S. OF TRINITY COLLEGE, CAMBRIDGE. 



REPRINTED, WITH THE AUTHOR'S ADDITIONS, FROM THE ATHEN-EUM 



SECOND EDITION 

EDITED BY 

DAVID EUGENE SMITH. 



"UT AGENDO SURGAMUS ARGUENDO GUSTAMUS." 

PTOCHODOKIARCHUS ANAGRAMMATISTES. 



VOLUME I. 



THE OPEN COURT PUBLISHING CO. 

CHICAGO LONDON 

1915 






AUTHORIZED EDITION 

COPYRIGHT IN GREAT BRITAIN UNDER THE ACT OF 191 I 
AND COPYRIGHT IN THE UNITED STATES BY 

THE OPEN COURT PUBLISHING COMPANY 
1915 



PREFACE TO THE FIRST EDITION. 

(1872) 

It is not without hesitation that I have taken upon my- 
self the editorship of a work left avowedly imperfect by 
the author, and, from its miscellaneous and discursive char- 
acter, difficult of completion with due regard to editorial 
limitations by a less able hand. 

Had the author lived to carry out his purpose he would 
have looked through his Budget again, amplifying and 
probably rearranging some of its contents. He had col- 
lected materials for further illustration of Paradox of the 
kind treated of in this book ; and he meant to write a 
second part, in which the contradictions and inconsisten- 
cies of orthodox learning would have been subjected to the 
same scrutiny and castigation as heterodox ignorance had 
already received. 

It will be seen that the present volume contains more 
than the Athenceum Budget. Some of the additions formed 
a Supplement to the original articles. These supplementary 
paragraphs were, by the author, placed after those to which 
they respectively referred, being distinguished from the rest 
of the text by brackets. I have omitted these brackets as 
useless, except where they were needed to indicate subse- 
quent writing. 

Another and a larger portion of the work consists of 
discussion of matters of contemporary interest, for the 
Budget was in some degree a receptacle for the author's 
thoughts on any literary, scientific, or social question. Hav- 



337853 



IV A BUDGET OF PARADOXES. 

ing grown thus gradually to its present size, the book as 
it was left was not quite in a fit condition for publication, 
but the alterations which have been made are slight and 
few, being in most cases verbal, and such as the sense 
absolutely required, or transpositions of sentences to secure 
coherence with the rest, in places where the author, in his 
more recent insertion of them, had overlooked the con- 
nection in which they stood. In no case has the meaning 
been in any degree modified or interfered with. 

One rather large omission must be mentioned here. It 
is an account of the quarrel between Sir James South and 
Mr. Troughton on the mounting, etc. of the equatorial tele- 
scope at Campden Hill. At some future time when the 
affair has passed entirely out of the memory of living 
Astronomers, the appreciative sketch, which is omitted in 
this edition of the Budget, will be an interesting piece of 
history and study of character. 1 

A very small portion of Mr. James Smith's circle-squar- 
ing has been left out, with a still smaller portion of Mr. De 
Morgan's answers to that Cyclometrical Paradoxer. 

In more than one place repetitions, which would have 
disappeared under the author's revision, have been allowed 
to remain, because they could not have been taken away 
without leaving a hiatus, not easy to fill up without damage 
to the author's meaning. 

I give these explanations in obedience to the rules laid 
down for the guidance of editors at page 15. 2 If any 
apology for the fragmentary character of the book be 
thought necessary, it may be found in the author's own 
words at page 281 of the second volume. 3 

1 See Mrs. De Morgan's Memoir of Augustus De Morgan, Lon- 
$tfi, 1882, p. 61. 

"In the first edition this reference was to page 11. 

3 In the first edition this read "at page 438," the work then ap- 
pearing in a single volume. 



PREFACE TO THE FIRST EDITION. V 

The publication of the Budget could not have been de- 
layed without lessening the interest attaching to the writer's 
thoughts upon questions of our own day. I trust that, in- 
complete as the work is compared with what it might have 
been, I shall not be held mistaken in giving it to the world. 
Rather let me hope that it will be welcomed as an old 
friend returning under great disadvantages, but bringing a 
pleasant remembrance of the amusement which its weekly 
appearance in the Athenaum gave to both writer and 
reader. 

The Paradoxes are dealt with in chronological order. 
This will be a guide to the reader, and with the alphabet- 
ical Index of Names, etc., will, I trust, obviate all difficulty 
of reference. 

SOPHIA DE MORGAN. 
6 MERTON ROAD, PRIMROSE HILL. 



PREFACE TO THE SECOND EDITION. 

If Mrs. De Morgan felt called upon to confess her hesi- 
tation at taking upon herself the labor of editing these Para- 
doxes, much more should one who was born two genera- 
tions later, who lives in another land and who was reared 
amid different influences, confess to the same feeling when 
undertaking to revise this curious medley. But when we 
consider the nature of the work, the fact that its present 
rarity deprives so many readers of the enjoyment of its de- 
licious satire, and the further fact that allusions that were 
commonplace a halfcentury ago are now forgotten, it is 
evident that some one should take up the work and perform 
it con amore. 

Having long been an admirer of De Morgan, having 
continued his work in the bibliography of early arithmetics, 
and having worked in his library among the books of which 
he was so fond, it is possible that the present editor, what- 
ever may be his other shortcomings, may undertake the 
labor with as much of sympathy as any one who is in a 
position to perform it. With this thought in mind, two 
definite rules were laid down at the beginning of the task: 
(1) That no alteration in the text should be made, save in 
slightly modernizing spelling and punctuation and in the 
case of manifest typographical errors ; (2) That when- 
ever a note appeared it should show at once its authorship, 
to the end that the material of the original edition might 
appear intact. 

In considering, however, the unbroken sequence of items 



PREFACE TO THE SECOND EDITION. Vll 

that form the Budget, it seems clear that readers would be 
greatly aided if the various leading topics were separated 
in some convenient manner. After considerable thought it 
was decided to insert brief captions from time to time that 
might aid the eye in selecting the larger subjects of the 
text. In some .parts of the work these could easily be taken 
from the original folio heads, but usually they had to be 
written anew. While, therefore, the present editor accepts 
the responsibility for the captions of the various subdivi- 
sions, he has endeavored to insert them in harmony with 
the original text. 

As to the footnotes, the first edition had only a few, 
some due to De Morgan himself and others to Mrs. De 
Morgan. In the present edition those due to the former 
are signed A. De M., and those due to Mrs. De Morgan 
appear with her initials, S. E. De M. For all other foot- 
notes the present editor is responsible. In preparing them 
the effort has been made to elucidate the text by supplying 
such information as the casual reader might wish as he 
passes over the pages. Hundreds of names are referred to 
in the text that were more or less known in England half 
a century ago, but are now forgotten there and were never 
familiar elsewhere. Many books that were then current 
have now passed out of memory, and much that agitated 
England in De Morgan's prime seems now like ancient his- 
tory. Even with respect to well-known names, a little in- 
formation as to dates and publications will often be wel- 
come, although the editor recognizes that it will quite as 
often be superfluous. In order, therefore, to derive the 
pleasure that should come from reading the Budget, the 
reader should have easy access to the information that the 
notes are intended to supply. That they furnish too much 
here and too little there is to be expected. They are a 
human product, and if they fail to serve their purpose in all 
respects it is hoped that this failure will not seriously inter- 
fere with the reader's pleasure. 



Vlll A BUDGET OF PARADOXES. 

In general the present editor has refrained from ex- 
pressing any opinions that would strike a discordant note 
in the reading of the text as De Morgan left it. The temp- 
tation is great to add to the discussion at various points, 
but it is a temptation to be resisted. To furnish such in- 
formation as shall make the reading more pleasant, rather 
than to attempt to improve upon one of the most delicious 
bits of satire of the nineteenth century, has been the editor's 
wish. It would have been an agreeable task to review the 
history of circle squaring, of the trisection problem, and 
of the duplication of the cube. This, however, would be to 
go too far afield. For the benefit of those who wish to in- 
vestigate the subject the editor can only refer to such works 
and articles as the following: F. Rudio, Archimedes, Huy- 
gens, Lambert, Legendre, mit einer Uebersicht iiber die 
Geschichte des Problemes von der Quadrat ur des Z irk els, 
Leipsic, 1892; Thomas Muir, "Circle," in the eleventh edi- 
tion of the Encyclopedia Britannica; the various histories 
of mathematics ; and to his own article on "The Incommen- 
surability of ?r" in Prof. J. W. A. Young's Monographs on 
Topics of Modern Mathematics, New York, 1911. 

The editor wishes to express his appreciation and thanks 
to Dr. Paul Carus, editor of The Monist and The Open 
Court for the opportunity of undertaking this work ; to 
James Earl Russell, LL.D., Dean of Teachers College, Co- 
lumbia University, for his encouragement in its prosecution ; 
to Miss Caroline Eustis Seely for her intelligent and pains- 
taking assistance in securing material for the notes ; and to 
Miss Lydia G. Robinson and Miss Anna A. Kugler for their 
aid and helpful suggestions in connection with the proof- 
sheets. Without the generous help of all five this work 
would have been impossible. 

DAVID EUGENE SMITH. 

TEACHERS COLLEGE, COLUMBIA UNIVERSITY. 



INTRODUCTORY. 

IF I had before me a fly and an elephant, having never seen 
more than one such magnitude of either kind ; and if the 
fly were to endeavor to persuade me that he was larger than 
the elephant, I might by possibility be placed in a difficulty. 
The apparently little creature might use such arguments 
about the effect of distance, and might appeal to such laws 
of sight and hearing as I, if unlearned in those things, might 
be unable wholly to reject. But if there were a thousand flies, 
all buzzing, to appearance, about the great creature ; and, to 
a fly, declaring, each one for himself, that he was bigger than 
the quadruped ; and all giving different and frequently con- 
tradictory reasons ; and each one despising and opposing the 
reasons of the others I should feel quite at my ease. I 
should certainly say, My little friends, the case of each one 
of you is destroyed by the rest. I intend to show flies in the 
swarm, with a few larger animals, for reasons to be given. 

In every age of the world there has been an established 
system, which has been opposed from time to time by iso- 
lated and dissentient reformers. The established system has 
sometimes fallen, slowly and gradually: it has either been 
upset by the rising influence of some one man, or it has been 
sapped by gradual change of opinion in the many. 

I have insisted on the isolated character of the dissen- 
tients, as an element of the a priori probabilities of the case. 
Show me a schism, especially a growing schism, and it is 
another thing. The homeopathists, for instance, shall be, if 
any one so think, as wrong as St. John Long ; but an organ- 



2 A BUDGET OF PARADOXES. 

ized opposition, supported by the efforts of many acting in 
concert, appealing to common arguments and experience, 
with perpetual succession and a common seal, as the Queen 
says in the charter, is, be the merit of the schism what it 
may, a thing wholly different from the case of the isolated 
opponent in the mode of opposition to it which reason points 
out. 

During the last two centuries and a half , physical knowl- 
edge has been gradually made to rest upon a basis which it 
had not before. It has become mathematical. The question 
now is, not whether this or that hypothesis is better or worse 
to the pure thought, but whether it accords with observed 
phenomena in those consequences which can be shown neces- 
sarily to follow from it, if it be true. Even in those sciences 
which are not yet under the dominion of mathematics, and 
perhaps never will be, a working copy of the mathematical 
process has been made. This is not known to the followers 
of those sciences who are not themselves mathematicians 
and who very often exalt their horns against the mathemat- 
ics in consequence. They might as well be squaring the 
circle, for any sense they show in this particular. 

A great many individuals, ever since the rise of the math- 
ematical method, have, each for himself, attacked its direct 
and indirect consequences. I shall not here stop to point out 
how the very accuracy of exact science gives better aim than 
the preceding state of things could give. I shall call each of 
these persons a paradoxer, and his system a paradox. I use 

v the word in the old sense : a paradox is something which is 
apart from general opinion, either in subject-matter, method, 
or conclusion. 

Many of the things brought forward would now be 
called crotchets, which is the nearest word we have to old 
paradox. But there is this difference, that by calling a thing 

^ a crotchet we mean to speak lightly of it ; which was not the 
necessary sense of paradox. Thus in the sixteenth century 
many spoke of the earth's motion as the paradox of Coper- 



INTRODUCTORY. O 

nicus, who held the ingenuity of that theory in very high 
esteem, and some, I think, who even inclined towards it. In 
the seventeenth century, the depravation of meaning took 
place, in England at least. Phillips says paradox is "a thing 
which seemeth strange" here is the old meaning: after a 
colon he proceeds "and absurd, and is contrary to com- 
mon opinion," which is an addition due to his own time. 

Some of my readers are hardly inclined to think that the 
word paradox could once have had no disparagement in its 
meaning; still less that persons could have applied it to 
themselves. I chance to have met with a case in point 
against them. It is Spinoza's Philosophia Scriptures Inter- 
pres, Exercitatio Paradoxa, printed anonymously at Eleu- 
theropolis, in 1666. This place was one of several cities in 
the clouds, to which the cuckoos resorted who were driven 
\ away by the other birds ; that is, a feigned place of printing, 
adopted by those who would have caught it if orthodoxy 
could have caught them. Thus, in 1656, the works of So- 
cinus could only be printed at Irenopolis. The author de- 
serves his self-imposed title, as in the following: 1 

"Quanto sane satius fuisset illam [Trinitatem] pro mys- 
terio non habuisse, et Philosophise ope, antequam quod esset 
statuerent, secundum verae logices prsecepta quid esset cum 
Cl. Kleckermanno investigasse ; tanto fervore ac labore in 
profundissimas speluncas et obscurissimos metaphysicarum 
speculationum atque fictionum recessus se recipere ut ab ad- 
versariorum telis sententiam suam in tuto collocarent. Pro- 

1 "Just as it would surely have been better not to have considered 
it (i.e., the trinity) as a mystery, and with Cl. Kleckermann to have 
investigated by the aid of philosophy according to the teaching of 
true logic what it might be, before they determined what it was ; 
just so would it have been better to withdraw zealously and indus- 
triously into the deepest caverns and darkest recesses of metaphys- 
ical speculations and suppositions in order to establish their opinion 
beyond danger from the weapons of their adversaries. .. .Indeed that 
great man so explains and demonstrates this dogma (although to 
theologians the word has not much charm) from the immovable 
foundations of philosophy, that with but few changes and additions 
a mind sincerely devoted to truth can desire nothing more." 



4 A BUDGET OF PARADOXES. 

fecto magnus ille vir. . . .dogma illud, quamvis apud theo- 
logos eo nomine non multum gratise iniverit, ita ex im- 
motis Philosophise fundamentis explicat ac demonstrat, ut 
paucis tantum immutatis, atque additis, nihil amplius animus 
veritate sincere deditus desiderare possit." 

This is properly paradox, though also heterodox. It 
supposes, contrary to all opinion, orthodox and heterodox, 
that philosophy can, with slight changes, explain the Atha- 
nasian doctrine so as to be at least compatible with ortho- 
doxy. The author would stand almost alone, if not quite ; 
and this is what he meant. I have met with the counter- 
paradox. I have heard it maintained that the doctrine as 
it stands, in all its mystery is a priori more likely than any 
other to have been Revelation, if such a thing were to be ; 
and that it might almost have been predicted. 

After looking into books of paradoxes for more than 
thirty years, and holding conversation with many persons 
who have written them, and many who might have done so, 
there is one point on which my mind is fully made up. The 
manner in which a paradoxer will show himself, as to sense 
or nonsense, will not depend upon what he maintains, but 
upon whether he has or has not made a sufficient knowledge 
of what has been done by others, especially as to the mode of 
doing it, a preliminary to inventing knowledge for himself. 
That a little knowledge is a dangerous thing is one of the 
most fallacious of proverbs. A person of small knowledge 
is in danger of trying to make his little do the work of more ; 
but a person without any is in more danger of making his 
no knowledge do the work of some. Take the speculations 
on the tides as an instance. Persons with nothing but a 
little geometry have certainly exposed themselves in their 
modes of objecting to results which require the higher math- 
ematics to be known before an independent opinion can be 
formed on sufficient grounds. But persons with no geom- 
etry at all have done the same thing much more completely. 



INTRODUCTORY. D 

There is a line to be drawn which is constantly put aside 
in the arguments held by paradoxers in favor of their right 
to instruct the world. Most persons must, or at least will, 
like the lady in Cadogan Place, 1 form and express an im- 
mense variety of opinions on an immense variety of sub- 
jects; and all persons must be their own guides in many 
things. So far all is well. But there are many who, in car- 
rying the expression of their own opinions beyond the usual 
tone of private conversation, whether they go no further 
than attempts at oral proselytism, or whether they commit 
themselves to the press, do not reflect that they have ceased 
to stand upon the ground on which their process is defen- 
sible. Aspiring to lead others, they have never given them- 
selves the fair chance of being first led by other others into 
something better than they can start for themselves ; and that 
they should first do this is what both those classes of others 
have a fair right to expect. New knowledge, when to any 
purpose, must come by contemplation of old knowledge in 
every matter which concerns thought ; mechanical contrivance 
sometimes, not very often, escapes this rule. All the men who 
are now called discoverers, in every matter ruled by thought, 
have been men versed in the minds of their predecessors, and 
learned in what had been before them. There is not one 
exception. I do not say that every man has made direct 
acquantance with the whole of his mental ancestry; many 
have, as I may say, only known their grandfathers by the 
report of their fathers. But even on this point it is remark- 
able how many of the greatest names in all departments of 
knowledge have been real antiquaries in their several sub- 
jects. 

I may cite, among those who have wrought strongly upon 
opinion or practice in science, Aristotle, Plato, Ptolemy, Eu- 
clid, Archimedes, Roger Bacon, Copernicus, Francis Bacon, 
Ramus, Tycho Brahe, Galileo, Napier, Descartes, Leibnitz, 
Newton, Locke. I take none but names known out of their 
1 Mrs. Wititterly, in Nicholas Nickleby.A. De M. 



6 A BUDGET OF PARADOXES. 

fields of work; and all were learned as well as sagacious. 
I have chosen my instances: if any one will undertake to 
show a person of little or no knowledge who has established 
himself in a great matter of pure thought, let him bring 
forward his man, and we shall see. 

This is the true way of putting off those who plague 
others with their great discoveries. The first demand made 
should be Mr. Moses, before I allow you to lead me over the 
Red Sea, I must have you show that you are learned in all 
the wisdom of the Egyptians upon your own subject. The 
plea that it is unlikely that this or that unknown person 
should succeed where Newton, etc. have failed, or should 
show Newton, etc. to be wrong, is utterly null and void. It 
was worthily versified by Sylvanus Morgan (the great her- 
ald who in his Sphere of Gentry gave coat armor to " Gentle- 
man Jesus," as he said), who sang of Copernicus as follows 
(1652): 

"If Tellus winged be, 

The earth a motion round; 

Then much deceived are they 

Who nere before it found. 

Solomon was the wisest, 

His wit nere this attained; 

Cease, then, Copernicus, 

Thy hypothesis is vain." 

Newton, etc. were once unknown ; but they made them- 
selves known by what they knew, and then brought forward 
what they could do ; which I see is as good verse as that of 
Herald Sylvanus. The demand for previous knowledge dis- 
poses of twenty-nine cases out of thirty, and the thirtieth 
is worth listening to. 

I have not set down Copernicus, Galileo, etc. among the 
paradoxers, merely because everybody knows them; if my 
list were quite complete, they would have been in it. But 
the reader will find Gilbert, the great precursor of sound 
magnetical theory ; and several others on whom no censure 
can be cast, though some of their paradoxes are inadmissible, 



INTRODUCTORY. / 

some unprovoked, and some capital jokes, true or false: the 
author of Vestiges of Creation is an instance. I expect that 
my old correspondent, General Perronet Thompson, will ad- 
mit that his geometry is part and parcel of my plan ; and 
also that, if that plan embraced politics, he would claim a 
place for his Catechism on the Corn Laws, a work at one 
time paradoxical, but which had more to do with the aboli- 
tion of the bread-tax than Sir Robert Peel. 

My intention in publishing this Budget in the Athenaeum 
is to enable those who have been puzzled by one or two dis- 
coverers to see how they look in a lump. The only question 
is, has the selection been fairly made ? To this my answer is, 
that no selection at all has been made. The books are, with- 
out exception, those which I have in my own library ; and I 
have taken all I mean all of the kind : Heaven forbid that 
I should be supposed to have no other books ! But I may 
have been a collector, influenced in choice by bias? I an- 
swer that I never have collected books of this sort that is, 
I have never searched for them, never made up my mind to 
look out for this book or that. I have bought what happened 
to come in my way at show or auction ; I have retained what 
came in as part of the undescribed portion of miscellaneous 
auction lots ; I have received a few from friends who found 
them among what they called their rubbish ; and I have pre- 
served books sent to me for review. In not a few instances 
the books have been bound up with others, unmentioned at 
the back ; and for years I knew no more I had them than I 
knew I had Lord Macclesfi eld's speech on moving the change 
of Style, which, after I had searched shops, etc. for it in 
vain, I found had been reposing on my own shelves for 
many years, at the end of a summary of Leibnitz's philos- 
ophy. Consequently, I may positively affirm that the fol- 
lowing list is formed by accident and circumstance alone, 
and that it truly represents the casualties of about a third 
of a century. For instance, the large proportion of works 



g A BUDGET OF PARADOXES. 

on the quadrature of the circle is not my doing: it is the 
natural share of this subject in the actual run of events. 

[I keep to my plan of inserting only such books as I pos- 
sessed in 1863, except by casual notice in aid of my remarks. 
I have found several books on my shelves which ought to 
have been inserted. These have their titles set out at the 
commencement of their articles, in leading paragraphs ; the 
casuals are without this formality. 1 ] 

Before proceeding to open the Budget, I say something 
on my personal knowledge of the class of discoverers who 
square the circle, upset Newton, etc. I suspect I know more 
of the English class than any man in Britain. I never kept 
any reckoning ; but I know that one year with another and 
less of late years than in earlier time I have talked to more 
than five in each year, giving more than a hundred and fifty 
specimens. Of this I am sure, that it is my own fault if they 
have not been a thousand. Nobody knows how they swarm, 
except those to whom they naturally resort. They are in all 
ranks and occupations, of all ages and characters. They 
are very earnest people, and their purpose is bona fide the 
dissemination of their paradoxes. A great many the mass, 
indeed are illiterate, and a great many waste their means, 
and are in or approaching penury. But I must say that 
never, in any one instance, has the quadrature of the circle, 
or the like, been made a pretext for begging; even to be 
asked to purchase a book is of the very rarest occurrence 
it has happened, and that is all. 

These discoverers despise one another : if there were the 
concert among them which there is among foreign mendi- 
cants, a man who admitted one to a conference would be 
plagued to death. I once gave something to a very genteel 
French applicant, who overtook me in the street, at my own 
door, saying he had picked up my handkerchief : whether he 
picked it up in my pocket for an introduction, I know not. 

*The brackets mean that the paragraph is substantially from 
some one of the Athen&um Supplements. S. E. De M. 



INTRODUCTORY. 

But that day week came another Frenchman to my house, 
and that day fortnight a French lady ; both failed, and I had 
no more trouble. The same thing happened with Poles. It 
is not so with circle-squarers, etc.: they know nothing of 
each other. Some will read this list, and will say I am right 
enough, generally speaking, but that there is an exception, 
if I could but see it. 

I do not mean, by my confession of the manner in which 
I have sinned against the twenty-four hours, to hold myself 
out as accessible to personal explanation of new plans. Quite 
the contrary : I consider myself as having made my report, 
and being discharged from further attendance on the sub- 
ject. I will not, from henceforward, talk to any squarer of 
the circle, trisector of the angle, duplicator of the cube, con- 
structor of perpetual motion, subverter of gravitation, stag- 
nator of the earth, builder of the universe, etc. I will receive 
any writings or books which require no answer, and read 
them when I please : I will certainly preserve them this list 
may be enlarged at some future time. 

There are three subjects which I have hardly anything 
upon ; astrology, mechanism, and the infallible way of win- 
ning at play. I have never cared to preserve astrology. The 
mechanists make models, and not books. The infallible win- 
ners though I have seen a few think their secret too val- 
uable, and prefer mutare quadrata rotundis to turn dice 
into coin at the gaming-house: verily they have their re- 
ward. 

I shall now select, to the mystic number seven, instances 
of my personal knowledge of those who think they have 
discovered, in illustration of as many misconceptions. 

1. Attempt by help of the old philosophy, the discoverer 
not being in possession of modern knowledge. A poor school- 
master, in rags, introduced himself to a scientific friend with 
whom I was talking, and announced that he had found out 
the composition of the sun. "How was that done?" "By 
consideration of the four elements." "What are they?" 



10 A BUDGET OF PARADOXES. 

"Of course, fire, air, earth, and water." "Did you not know 
that air, earth, and water, have long been known to be no 
elements at all, but compounds?" "What do you mean, 
sir? Who ever heard of such a 'thing?" 

2. The notion that difficulties are enigmas, to be over- 
come in a moment by a lucky thought. A nobleman of very 
high rank, now long dead, read an article by me on the 
quadrature, in an early number of the Penny Magazine. He 
had, I suppose, school recollections of geometry. He put 
pencil to paper, drew a circle, and constructed what seemed 
likely to answer, and, indeed, was as he said certain, if 
only this bit were equal to that ; which of course it was not. 
He forwarded his diagram to the Secretary of the Diffusion 
Society, to be handed to the author of the article, in case the 
difficulty should happen to be therein overcome. 

3. Discovery at all hazards, to get on in the world. Thirty 
years ago, an officer of rank, just come from foreign service, 
and trying for a decoration from the Crown, found that his 
claims were of doubtful amount, and was told by a friend 
that so and so, who had got the order, had the additional 
claim of scientific distinction. Now this officer, while abroad, 
had bethought himself one day, that there really could be 
no difficulty in finding the circumference of a circle: if a 
circle were rolled upon a straight line until the undermost 
point came undermost again, there would be the straight 
line equal to the circle. He came to me, saying that he did 
not feel equal to the statement of his claim in this respect, 

,but that if some clever fellow would put the thing in a 
proper light, he thought his affair might be managed. I was 
clever enough to put the thing in a proper light to himself, 
to this extent at least, that, though perhaps they were wrong, 
the advisers of the Crown would never put the letters K.C.B. 
to such a circle as his. 

4. The notion that mathematicians cannot find the circle 
for common purposes. A working man measured the alti- 
tude of a cylinder accurately, and I think the process of 



INTRODUCTORY. 1 1 

Archimedes was one of his proceedings found its bulk. 
He then calculated the ratio of the circumference to the 
diameter, and found it answered very well on other modes 
of trial. His result was about 3 . 14. He came to London, 
and somebody sent him to me. Like many others of his pur- 
suit, he seemed to have turned the whole force of his mind 
upon one of his points, on which alone he would be open to 
refutation. He had read some of Kater's experiments, and 
had got the Act of 1825 on weights and measures. Say what 
I would, he had for a long time but one answer "Sir ! I go 
upon Captain Kater and the Act of Parliament." But I 
fixed him at last. I happened to have on the table a proof- 
sheet of the Astronomical Memoirs, in which were a large 
number of observed places of the planets compared with 
prediction, and asked him whether it could be possible that 
persons who did not know the circle better than he had 
found it could make the calculations, of which I gave him 
a notion, so accurately? He was perfectly astonished, and 
took the titles of some books which he said he would read. 

5. Application for the reward from abroad. Many years 
ago, about twenty-eight, I think, a Jesuit came from South 
America, with a quadrature, and a cutting from a news- 
paper, announcing that a reward was ready for the discovery 
in England. On this evidence he came over. After satis- 
fying him that nothing had ever been offered here, I dis- 
cussed his quadrature, which was of no use. I succeeded 
better when I told him of Richard White, also a Jesuit, and 
author of a quadrature published before 1648, under the 
name of Chryscespis, of which I can give no account, having 
never seen it. This White (Albius) is the only quadrator 
who was ever convinced of his error. My Jesuit was struck 
by the instance, and promised to read more geometry he 
was no Clavius before he published his book. He relapsed, 
however, for I saw his book advertised in a few days. I 
may say, as sufficient proof of my being no collector, that I 
had not the curiosity to buy his book; and my friend the 



12 A BUDGET OF PARADOXES. 

Jesuit did not send me a copy, which he ought to have done, 
after the hour I had given him. 

6. Application for the reward at home. An agricultural 
laborer squared the circle, and brought the proceeds to Lon- 
don. He left his papers with me, one of which was the copy 
of a letter to the Lord Chancellor, desiring his Lordship to 
hand over forthwith 100,000 pounds, the amount of the 
alleged offer of reward. He did not go quite so far as M. 
de Vausenville, who, I think in 1778, brought an action 
against the Academy of Sciences to recover a reward to 
which he held himself entitled. I returned the papers, with 
a note, stating that he had not the knowledge requisite to 
see in what the problem consisted. I got for answer a letter 
in which I was told that a person who could not see that he 
had done the thing should "change his business, and appro- 
priate his time and attention to a Sunday-school, to learn 
what he could, and keep the litle children from durting their 
close" I also received a letter from a friend of the quad- 
rator, informing me that I knew his friend had succeeded, 
and had been heard to say so. These letters were printed 
without the names of the writers for the amusement of the 
readers of Notes and Queries, First Series, xii. 57, and they 
will appear again in the sequel. 

[There are many who have such a deep respect for any 
attempt at thought that they are shocked at ridicule even of 
those who have made themselves conspicuous by pretending 
to lead the world in matters which they have not studied. 
Among my anonyms is a gentleman who is angry at my 
treatment of the "poor but thoughtful" man who is described 
in my introduction as recommending me to go to a Sunday- 
school because I informed him that he did not know in what 
the difficulty of quadrature consisted. My impugner quite 
forgets that this man's "thoughtfulness" chiefly consisted 
in his demanding a hundred thousand pounds from the Lord 
Chancellor for his discovery ; and I may add, that his great- 
est stretch of invention was finding out that "the clergy" 



INTRODUCTORY. 13 

were the means of his modest request being unnoticed. I 
mention this letter because it affords occasion to note a very 
common error, namely, that men unread in their subjects 
have, by natural wisdom, been great benefactors of man- 
kind. My critic says, "Shakspeare, whom the Pror (sic) 
may admit to be a wisish man, though an object of con- 
tempt as to learning. ..." Shakespeare an object of con- 
tempt as to learning! Though not myself a thoroughgoing 
Shakespearean and adopting the first half of the opinion 
given by George III, "What! is there not sad stuff? only 
one must not say so" I am strongly of opinion that he throws 
out the masonic signs of learning in almost every scene, to 
all who know what they are. And this over and above every 
kind of direct evidence. First, foremost, and enough, the 
evidence of Ben Jonson that he had "little Latin and less 
Greek" ; then Shakespeare had as much Greek as Jonson 
would call some, even when he was depreciating. To have 
any Greek at all was in those days exceptional. In Shake- 
speare's youth St. Paul's and Merchant Taylor's schools 
were to have masters learned in good and clean Latin litera- 
ture, and also in Greek if such may be gotten. When Jonson* 
spoke as above, he intended to put Shakespeare low among 
the learned, but not out of their pale ; and he spoke as a rival 
dramatist, who was proud of his own learned sock ; and it 
may be a subject of inquiry how much Latin he would call 
little. If Shakespeare's learning on certain points be very 
much less visible than Jonson's, it is partly because Shake- 
speare's writings hold it in chemical combination, Jonson's 
in mechanical aggregation.] 

7. An elderly man came to me to show me how the uni- 
verse was created. There was one molecule, which by vibra- 
tion became Heaven knows how! the Sun. Further 
vibration produced Mercury, and so on. I suspect the nebu- 
lar hypothesis had got into the poor man's head by reading, 
in some singular mixture with what it found there. Some 
modifications of vibration gave heat, electricity, etc. I lis- 



14 A BUDGET OF PARADOXES. 

tened until my informant ceased to vibrate which is always 
the shortest way and then said, "Our knowledge of elastic 
fluids is imperfect." "Sir!" said he, "I see you perceive 
the truth of what I have said, and I will reward your atten- 
tion by telling you what I seldom disclose, never, except to 
those who can receive my theory the little molecule whose 
vibrations have given rise to our solar system is the Logos 
of St. John's Gospel!" He went away to Dr. Lardner, 
who would not go into the solar system at all the first 
molecule settled the question. So hard upon poor discov- 
erers are men of science who are not antiquaries in their 
subject! On leaving, he said, "Sir, Mr. De Morgan re- 
ceived me in a very different way! he heard me attentively, 
and I left him perfectly satisfied of the truth of my system." 
I have had much reason to think that many discoverers, of 
all classes, believe they have convinced every one who is 
not peremptory to the verge of incivility. 

My list is given in chronological order. My readers will 
understand that my general expressions, where slighting 
or contemptuous, refer to the ignorant, who teach before 
they have learned. In every instance, those of whom I am 
able to speak with respect, whether as right or wrong, have 
sought knowledge in the subject they were to handle before 
they completed their speculations. I shall further illustrate 
this at the conclusion of my list 

Before I begin the list, I give prominence to the follow- 
ing letter, addressed by me to the Correspondent of October 
28, 1865. Some of my paradoxers attribute to me articles 
in this or that journal ; and others may think I know some 
do think they know me as the writer of reviews of some 
of the very books noticed here. The following remarks will 
explain the way in which they may be right, and in which 
they may be wrong. 



INTRODUCTORY. 



THE EDITORIAL SYSTEM. 



15 



"SiR, I have reason to think that many persons have a 
very inaccurate notion of the Editorial System. What I call 
by this name hc.s grown up in the last centenary a word I 
may use to signify the hundred years now ending, and to 
avoid the ambiguity of century. It cannot conveniently be 
explained by editors themselves, and edited journals gen- 
erally do not like to say much about it. In your paper 
perhaps, in which editorial duties differ somewhat from 
those of ordinary journals, the common system may be 
freely spoken of. 

"When a reviewed author, as very often happens, writes 
to the editor of the reviewing journal to complain of what 
has been said of him, he frequently even more often than 
not complains of 'your reviewer/ He sometimes presumes 
that 'you' have, 'through inadvertence' in this instance, 'al- 
lowed some incompetent person to lower the character of 
your usually accurate pages.' Sometimes he talks of 'your 
scribe,' and, in extreme cases, even of 'your hack.' All this 
shows perfect ignorance of the journal system, except where 
it is done under the notion of letting the editor down easy. 
But the editor never accepts the mercy. 

"All that is in a journal, except what is marked as from 
a correspondent, either by the editor himself or by the cor- 
respondent's real or fictitious signature, is published entirely 
on editorial responsibility, as much as if the editor had writ- 
ten it himself. The editor, therefore, may claim, and does 
claim and exercise, unlimited right of omission, addition, 
and alteration. This is so well understood that the editor 
performs his last function on the last revise without the 
'contributor' knowing what is done. The word contributor 
is the proper one ; it implies that he furnishes materials with- 
out stating what he furnishes or how much of it is accepted, 
or whether he be the only contributor. All this applies both 
to political and literary journals. No editor acknowledges 



16 A BUDGET OF PARADOXES. 

the right of a contributor to withdraw an article, if he should 
find alterations in the proof sent to him for correction which 
would make him wish that the article should not appear. If 
the demand for suppression were made I say nothing about 
what might be granted to request the answer would be, It 
is not your article, but mine ; I have all the responsibility ; if 
it should contain a libel, I could not give you up, even at 
your own desire. You have furnished me with materials, 
on the known and common understanding that I was to use 
them at my discretion, and you have no right to impede my 
operations by making the appearance of the article depend 
on your approbation of my use of your materials/ 

"There is something to be said for this system, and some- 
thing against it I mean simply on its own merits. But the 
all-conquering argument in its favor is, that the only prac- 
ticable alternative is the modern French plan of no articles 
without the signature of the writers. I need not discuss this 
plan ; there is no collective party in favor of it. Some may 
think it is not the only alternative ; they have not produced 
any intermediate proposal in which any dozen of persons have 
concurred. Many will say, Is not all this, though perfectly 
correct, well known to be matter of form? Is it not prac- 
tically the course of events that an engaged contributor 
writes the article, and sends it to the editor, who admits it 
as written substantially, at least? And is it not often very 
well known, by style and in other ways, who it was wrote 
the article? This system is matter of form just as much 
as loaded pistols are matter of form so long as the wearer 
is not assailed ; but matter of form takes the form of matter 
in the pulling of a trigger, so soon as the need arises. Edi- 
tors and contributors who can work together find each other, 
out by elective affinity, so that the common run of events 
settles down into most articles appearing much as they are 
written. And there are two safety-valves ; that is, when 
judicious persons come together. In the first place, the edi- 
tor himself, when he has selected his contributor, feels that 



INTRODUCTORY. 17 

the contributor is likely to know his business better than an 
editor can teach him ; in fact, it is on that principle that the 
selection is made. But he feels that he is more competent 
than the writer to judge questions of strength and of tone, 
especially when the general purpose of the journal is con- 
sidered, of which the editor is the judge without appeal. An 
editor who meddles with substantive matter is likely to be 
wrong, even when he knows the subject; but one who prunes 
what he deems excess, is likely to be right, even when he 
does not know the subject. In the second place, a contrib- 
utor knows that he is supplying an editor, and learns, with- 
out suppressing truth or suggesting falsehood, to make the 
tone of his communications suit the periodical in which they 
are to appear. Hence it very often arises that a reviewed 
author, who thinks he knows the name of his reviewer, and 
proclaims it with expressions of dissatisfaction, is only 
wrong in supposing that his critic has given all his mind. 
It has happened to myself more than once, to be announced 
as the author of articles which I could not have signed, be- 
cause they did not go far enough to warrant my affixing my 
name to them as to a sufficient expression of my own opin- 
ion. 

"There are two other ways in which a reviewed author 
may be wrong about his critic. An editor frequently makes 
slight insertions or omissions I mean slight in quantity of 
type as he goes over the last proof ; this he does in a com- 
parative hurry, and it may chance that he does not know the 
full sting of his little alteration. The very bit which the 
writer of the book most complains of may not have been seen 
by the person who is called the writer of the article until 
after the appearance of the journal ; nay, if he be one of those 
few, I daresay who do not read their own articles, may 
never have been seen by him at all. Possibly, the insertion 
or omission would not have been made if the editor could 
have had one minute's conversation with his contributor. 
Sometimes it actually contradicts something which is al- 



18 'A BUDGET OF PARADOXES. 

lowed to remain in another part of the article; and some- 
times, especially in the case of omission, it renders other 
parts of the article unintelligible. These are disadvantages 
of the system, and a judicious editor is not very free with 
his unus et alter pannus. Next, readers in general, when 
they see the pages of a journal with the articles so nicely 
fitting, and so many ending with the page or column, have 
very little notion of the cutting and carving which goes to 
the process. At the very last moment arises the necessity 
of some trimming of this kind ; and the editor, who would 
gladly call the writer to counsel if he could, is obliged to 
strike out ten or twelve lines. He must do his best, but it 
may chance that the omission selected would take from the 
writer the power of owning the article. A few years ago, 
an able Opponent of mine wrote to a journal some criticisms 
upon an article which he expressly attributed to me. I re- 
plied as if I were the writer, which, in a sense, I was. But 
if any one had required of me an unmodified 'Yes' or 'No' 
to the question whether I wrote the article, I must, of two 
falsehoods, have chosen 'No': for certain omissions, dictated 
by the necessities of space and time, would have amounted, 
had my signature been affixed, to a silent surrender of points 
which, in my own character, I must have strongly insisted 
on, unless I had chosen to admit certain inferences against 
what I had previously published in my own name. I may 
here add that the forms of journalism obliged me in this 
case to remind my opponent that it could not be permitted to 
me, in that journal, either to acknowledge or deny the 
authorship of the articles. The cautions derived from the 
above remarks are particularly wanted with reference to the 
editorial comments upon letters of complaint. There is often 
no time to send these letters to the contributor, and even 
when this can be done, an editor is and very properly 
never of so editorial a mind as when he is revising the com- 
ments of a contributor upon an assailant of the article. He 
is then in a better position as to information, and a more 



INTRODUCTORY. 19 

critical position as to responsibility. Of course, an editor 
never meddles, except under notice, with the letter of a cor- 
respondent, whether of a complainant, of a casual informant, 
or of a contributor who sees reason to become a correspond- 
ent. Omissions must sometimes be made when a grievance 
is too highly spiced. It did once happen to me that a wag- 
gish editor made an insertion without notice in a letter 
signed by me with some fiction, which insertion contained 
the name of a friend of mine, with a satire which I did 
not believe, and should not have written if I had. To my 
strong rebuke, he replied 'I know it was very wrong ; but 
human nature could not resist/ But this was the only occa- 
sion on which such a thing ever happened to me. 

"I daresay what I have written may give some of your 
readers to understand some of the pericula et commoda of 
modern journalism. I have known men of deep learning 
and science as ignorant of the prevailing system as any un- 
educated reader of a newspaper in a country town. I may 
perhaps induce some writers not to be too sure about 
this, that, or the other person. They may detect their re- 
viewer, and they may be safe in attributing to him the gen- 
eral matter and tone of the article. But about one and 
another point, especially if it be a short and stinging point, 
they may very easily chance to be wrong. It has happened 
to myself, and within a few weeks to publication, to be 
wrong in two ways in reading a past article to attribute 
to editorial insertion what was really my own, and to at- 
tribute to myself what was really editorial insertion." 

What is a man to do who is asked whether he wrote an 
article? He may, of course, refuse to answer; which is re- 
garded as an admission. He may say, as Swift did to Ser- 
jeant Bettesworth, "Sir, when I was a young man, a friend 
of mine advised me, whenever I was asked whether I had 
written a certain paper, to deny it; and I accordingly tell 
you that I did not write it." He may say, as I often do, 



20 A BUDGET OF PARADOXES. 

when charged with having invented a joke, story, or epi- 
gram, "I want all the credit I can get, and therefore I always 
acknowledge all that is attributed to me, truly or not; the 
story, etc. is mine." But for serious earnest, in the matter of 
imputed criticism, the answer may be, "The article was of 
my material, but the editor has not let it stand as I gave it ; 
I cannot own it as a whole." He may then refuse to be 
particular as to the amount of the editor's interference. Of 
this there are two extreme cases. The editor may have ex- 
punged nothing but a qualifying adverb. Or he may have 
done as follows. We all remember the account of Adam 
which satirizes woman, but eulogizes her if every second and 
third line be transposed. As in : 

"Adam could find no solid peace 

When Eve was given him for a mate, 
Till he beheld a woman's face, 
Adam was in a happy state." 

If this had been the article, and a gallant editor had made 
the transpositions, the author could not with truth acknowl- 
edge. If the alteration were only an omitted adverb, or a 
few things of the sort, the author could not with truth deny. 
In all that comes between, every man must be his own casuist. 
I stared, when I was a boy, to hear grave persons approve 
of Sir Walter Scott's downright denial that he was the 
author of Waverley, in answer to the Prince Regent's down- 
right question. If I remember rightly, Samuel Johnson 
would have approved of the same course. 

It is known that, whatever the law gives, it also gives 
all that is necessary to full possession; thus a man whose 
land is environed by land of others has a right of way 
over the land of these others. By analogy, it is argued that 
when a man has a right to his secret, he has a right to all 
that is necessary to keep it, and that is not unlawful. If, 
then, he can only keep his secret by denial, he has a right to 
denial. This I admit to be an answer against all men except 
the denier himself ; if conscience and self-respect 'will allow 



INTRODUCTORY. 21 

it, no one can impeach it. But the question cannot be solved 
on a case. That question is, A lie, is it malum in se, without 
reference to meaning and circumstances ? This is a question 
with two sides to it. Cases may be invented in which a lie 
is the only way of preventing a murder, or in which a lie 
may otherwise save a life. In these cases it is difficult to 
acquit, and almost impossible to blame; discretion intro- 
duced, the line becomes very hard to draw. 

I know but one work which has precisely as at first 
appears the character and object of my Budget. It is the 
Review of the Works of the Royal Society of London, by 
Sir John Hill, M.D. (1751 and 1780, 4to.). This man 
offended many : the Royal Society, by his work, the medical 
profession, by inventing and selling extra-pharmacopoeian 
doses ; Garrick, by resenting the rejection of a play. So 
Garrick wrote: 

"For physic and farces his equal there scarce is ; 
His farces are physic ; his physic a farce is." 

I have fired at the Royal Society and at the medical pro- 
fession, but I have given a wide berth to the drama and its 
wits ; so there is no epigram out against me, as yet. He was 
very able and very eccentric. Dr. Thomson (Hist. Roy. 
Soc.) says he has no humor, but Dr. Thomson was a man 
who never would have discovered humor. 

Mr. Weld (Hist. Roy. Soc.) backs Dr. Thomson, but 
with a remarkable addition. Having followed his prede- 
cessor in observing that the Transactions in Martin Folkes's 
time have an unusual proportion of trifling and puerile pa- 
pers, he says that Hill's book is a poor attempt at humor, 
and glaringly exhibits the feelings of a disappointed man. 
It is probable, he adds, that the points told with some effect 
on the Society ; for shortly after its publication the Trans- 
actions possess a much higher scientific value. 

I copy an account which I gave elsewhere. 

When the Royal Society was founded, the Fellows set 



22 A BUDGET OF PARADOXES. 

to work to prove all things, that they might hold fast that 
which was good. They bent themselves to the question 
whether sprats were young herrings. They made a circle 
of the powder of a unicorn's horn, and set a spider in the 
middle of it; "but it immediately ran out." They tried 
several times, and the spider "once made some stay in the 
powder." They inquired into Kenelm Digby's sympathetic 
powder. "Magnetic cures being discoursed of, Sir Gilbert 
Talbot promised to communicate what he knew of sympa- 
thetical cures ; and those members who had any of the 
powder of sympathy, were desired to bring some of it at 
the next meeting." 

June 21, 1661, certain gentlemen were appointed "cura- 
tors of the proposal of tormenting a man with the sympa- 
thetic powder" ; I cannot find any record of the result. And 
so they went on until the time of Sir John Hill's satire, in 
1751. This once well-known work is, in my judgment, the 
greatest compliment the Royal Society ever received. It 
brought forward a number of what are now feeble and 
childish researches in the Philosophical Transactions. It 
showed that the inquirers had actually been inquiring; and 
that they did not pronounce decision about "natural knowl- 
edge" by help of "natural knowledge." But for this, Hill 
would neither have known what to assail, nor how. Mat- 
ters are now entirely changed. The scientific bodies are far 
too well established to risk themselves. Ibit qui zonam 
perdidit : 

"Let him take castles who has ne'er a groat." 

These great institutions are now without any collective 
purpose, except that of promoting individual energy; they 
print for their contributors, and guard themselves by a gen- 
eral declaration that they will not be answerable for the 
things they print. Of course they will not put forward 
anything for everybody; but a writer of a certain reputa- 
tion, or matter of a certain look of plausibility and safety, 



INTRODUCTORY. 23 

will find admission. This is as it should be ; the pasturer of 
flocks and herds and the hunters of wild beasts are two very 
different bodies, with very different policies. The scien- 
tific academies are what a spiritualist might call "publishing 
mediums," and their spirits fall occasionally into writing 
which looks as if minds in the higher state were not always 
impervious to nonsense. 

The following joke is attributed to Sir John Hill. I 
cannot honestly say I believe it ; but it shows that his con- 
temporaries did not believe he had no humor. Good stories 
are always in some sort of keeping with the characters on 
which they are fastened. Sir John Hill contrived a com- 
munication to the Royal Society from Portsmouth, to the 
effect that a sailor had broken his leg in a fall from the 
mast-head ; that bandages and a plentiful application of tar- 
water had made him, in three days, able to use his leg as 
well as ever. While this communication was under grave 
discussion it must be remembered that many then thought 
tarwater had extraordinary remedial properties the joker 
contrived that a second letter should be delivered, which 
stated that the writer had forgotten, in his previous com- 
munication, to mention that the leg was a wooden leg! 
Horace Walpole told this story, I suppose for the first time ; 
he is good authority for the fact of circulation, but for 
nothing more. 

Sir John Hill's book is droll and cutting satire. Dr. 
Maty, (Sec. Rpyal Society) wrote thus of it in the Journal 
Britannique (Feb. 1751), of which he was editor: 

"II est facheux que cet ingenieux Naturaliste, qui nous 
a deja donne et qui nous prepare encore des ouvrages plus 
utiles, emploie a cette odieuse tache une plume qu'il trempe 
dans le fiel et dans 1'absinthe. II est vrai que plusieurs de 
ses remarques sont fondees, et qu'a 1'erreur qu'il indique, il 
joint en meme terns la correction. Mais il n'est pas tou- 
jours equitable, et ne manque jamais d'insulter. Que peut 



24 A BUDGET OF PARADOXES. 

apres tout prouver son livre, si ce n'est que la quarante- 
cinquieme partie d'un tres-ample et tres-utile Recueil n'est 
pas exempte d'erreurs? Devoit-il confondre avec des Ecri- 
vains superficiels, dont la Liberte du Corps ne permet pas de 
restreindre la fertilite, cette foule de savans du Premier 
ordre, dont les Ecrits ont orne et ornent encore les Trans- 
actions? A-t-il oublie qu'on y a vu frequemment les noms 
des Boyle, des Newton, des Halley, des De Moivres, des 
Hans Sloane, etc.? Et qu'on y trouve encore ceux des 
Ward, des Bradley, des Graham, des Ellicot, des Watson, 
et d'un Auteur que Mr. Hill prefere a tous les autres, je 
veux dire de Mr. Hill lui-meme?" 1 

This was the only answer ; but it was no answer at all. 
Hill's object was to expose the absurdities ; he therefore col- 
lected the absurdities. I feel sure that Hill was a benefactor 
of the Royal Society; and much more than he would have 
been if he had softened their errors and enhanced their 
praises. No reviewer will object to me that I have omitted 
Young, Laplace, etc. But then my book has a true title. 
Hill should not have called his a review of the "Works." 

It was charged against Sir John Hill that he had tried to 
become a Fellow of the Royal Society and had failed. This 
he denied, and challenged the production of the certificate 
which a candidate always sends in ; and which is preserved. 

1 "It is annoying that this ingenious naturalist who has already 
given us more useful works and has still others in preparation, uses 
for this odious task, a pen dipped in gall and wormwood. It is true 
that many of his remarks have some foundation, and that to each 
error that he points out he at the same time adds its correction. But 
he is not always just and never fails to insult. After all, what does 
his book prove except that a forty-fifth part of a very useful review 
is not free from mistakes? Must we confuse him with those super- 
ficial writers whose liberty of body does not permit them to restrain 
their fruitfulness, that crowd of savants of the highest rank whose 
writings have adorned and still adorn the Transactions? Has he 
forgotten that the names of the Boyles, Newtons, Halleys, De Moi- 
vres, Hans Sloanes, etc. have been seen frequently? and that still are 
found those of the Wards, Bradleys, Grahams, Ellicots, Watsons, 
and of an author whom Mr. Hill prefers to all others, I mean Mr. 
Hill himself?" 



INTRODUCTORY. 25 

But perhaps he could not get so far as a certificate that is, 
could not find any one to recommend him ; he was a likely 
man to be in such a predicament. As I have myself run foul 
of the Society on some little points, I conceive it possible that 
I may fall under a like suspicion. Whether I could have 
been a Fellow, I cannot know; as the gentleman said who 
was asked if he could play the violin, I never tried. I have 
always had a high opinion of the Society upon its whole his- 
tory. A person used to historical inquiry learns to look at 
wholes ; the Universities of Oxford and Cambridge, the Col- 
lege of Physicians, etc. are taken in all their duration. But 
those who are not historians I mean not possessed of the 
habit of history hold a mass of opinions about current 
things which lead them into all kinds of confusion when they 
try to look back. Not to give an instance which will offend 
any set of existing men this merely because I can do with- 
out it let us take the country at large. Magna Charta for 
ever ! glorious safeguard of our liberties ! Nullus liber homo 
capiatur out imprisonetur. . . .aut aliquo modo destruatur, 
nisi per judicium parium . . . . 1 Liber homo ; frank home ; a 
capital thing for him but how about the villeins'? Oh, 
there are none now\ But there were. Who cares for vil- 
lains, or barbarians, or helots ? And so England, and Athens, 
and Sparta, were free States ; all the freemen in them were 
free. Long after Magna Charta, villains were sold with 
their "chattels and offspring," named in that order. Long 
after Magna Charta, it was law that "Le Seigniour poit 
rob, naufrer, et chastiser son villein a son volunt, salve que 
il ne poit luy maim." 2 

The Royal Society was founded as a co-operative fcody, 
and co-operation was its purpose. The early charters, etc. 
do not contain a trace of the intention to create a scientific 
distinction, a kind of Legion of Honor. It is clear that the 

1 Let no free man be seized or imprisoned or in any way harmed 
except by trial of his peers." 

"The master can rob, wreck and punish his slave according to 
his pleasure save only that he may not maim him." 



26 A BUDGET OF PARADOXES. 

qualification was ability and willingness to do good work 
for the promotion of natural knowledge, no matter in how 
many persons, nor of what position in society. Charles II 
gave a smart rebuke for exclusiveness, as elsewhere men- 
tioned. In time arose, almost of course, the idea of distinc- 
tion attaching to the title; and when I first began to know 
the Society, it was in this state. Gentlemen of good social 
position were freely elected if they were really educated 
men ; but the moment a claimant was announced as resting 
on his science, there was a disposition to inquire whether he 
was scientific enough. The maxim of the poet was adopted ; 
and the Fellows were practically divided into Drink-deeps 
and Taste-nots. 

I was, in early life, much repelled by the tone taken by 
the Fellows of the Society with respect to their very mixed 
body. A man high in science some thirty-seven years ago 
(about 1830) gave me some encouragement, as he thought. 
"We shall have you a Fellow of the Royal Society in time," 
said he. Umph ! thought I : for I had that day heard of sonic 
recent elections, the united science of which would not have 
demonstrated I. 1, nor explained the action of a pump. 
Truly an elevation to look up at! It came, further, to my 
knowledge that the Royal Society if I might judge by the 
claims made by very influential Fellows considered itself 
as entitled to the best of everything: second-best being left 
for the newer bodies. A secretary, in returning thanks for 
the Royal at an anniversary of the Astronomical, gave rather 
a lecture to the company on the positive duty of all present 
to send the very best to the old body, and the absolute right 
of the old body to expect it. An old friend of mine, on a 
similar occasion, stated as a fact that the thing was always 
done, as well as that it ought to be done. 

Of late years this pretension has been made by a Presi- 
dent of the Society. In 1855, Lord Rosse presented a con- 
fidential memorandum to the Council on the expediency of 
enlarging their number. He says, "In a Council so small it 



INTRODUCTORY. 27 

is impossible to secure a satisfactory representation of the 
leading scientific Societies, and it is scarcely to be expected 
that, under such circumstances, they will continue to publish 
inferior papers while they send the best to our Transact ions." 
And, again, with all the Societies represented on the 
Council, "even if every Science had its Society, and if they 
published everything, withholding their best papers [i. e., 
from the Royal Society], which they would not be likely to 
do, still there would remain to the Royal Society. . ." Lord 
Rosse seems to imagine that the minor Societies themselves 
transfer their best papers to the Royal Society ; that if, for 
instance, the Astronomical Society were to receive from A. B. 
a paper of unusual merit, the Society would transfer it to 
the Royal Society. This is quite wrong: any preference of 
the Royal to another Society is the work of the contrib- 
utor himself. But it shows how well hafted is the Royal 
Society's claim, that a President should acquire the notion 
that it is acknowledged and acted upon by the other Socie- 
ties, in their joint and corporate capacities. To the preten- 
sion thus made I never could give any sympathy. When I 
first heard Mr. Christie, Sec. R. S., set it forth at the anni- 
versary dinner of the Astronomical Society, I remembered 
the Baron in Walter Scott : 

"Of Gilbert the Galliard a heriot he sought, 
Saying, Give thy best steed as a vassal ought." 

And I remembered the answer: 

"Lord and Earl though thou be, I trow 
I can rein Buck's-foot better than thou." 

Fully conceding that the Royal Society is entitled to pre- 
eminent rank and all the respect due to age and services, I 
could not, nor can I now, see any more obligation in a con- 
tributor to send his best to that Society than he can make out 
to be due to himself. This pretension, in my mind, was 
hooked on, by my historical mode of viewing things already 
mentioned, to my knowledge of the fact that the Royal So- 



28 A BUDGET OF PARADOXES. 

ciety the chief fault, perhaps, lying with its President, Sir 
Joseph Banks had sternly set itself against the formation 
of other societies ; the Geological and Astronomical, for in- 
stance, though it must be added that the chief rebels came 
out of the 'Society itself. And so a certain not very defined 
dislike was generated in my mind an anti-aristocratic affair 
to the body which seemed to me a little too uplifted. This 
would, I daresay, have worn off ; but a more formidable ob- 
jection arose. My views of physical science gradually ar- 
ranged themselves into a form which would have rendered 
F.R.S., as attached to my name, a false representation sym- 
bol. The Royal Society is the great fortress of general phys- 
ics : and in the philosophy of our day, as to general physics, 
there is something which makes the banner of -the R.S. one 
under which I cannot march. Everybody who saw the three 
letters after my name would infer certain things as to my 
mode of thought which would not be true inference. It 
would take much space to explain this in full. I may here- 
after, perhaps, write a budget of collected results of the 
a priori philosophy, the nibbling at the small end of om- 
niscience, and the effect it has had on common life, from 
the family parlor to the jury-box, from the girls'-school to 
the vestry-meeting. There are in the Society those who 
would, were there no others, prevent my criticism, be its 
conclusions true or false, from having any basis; but they 
are in the minority. 

There is no objection to be made to the principles of 
philosophy in vogue at the Society, when they are stated as 
principles; but there is an omniscience in daily practice 
which the principles repudiate. In like manner, the most 
retaliatory Christians have a perfect form of round words 
about behavior to those who injure them ; none of them are 
as candid as a little boy I knew, who, to his mother's admo- 
nition, You should love your enemies, answered Catch me 
at it! 

Years ago, a change took place which would alone have 



INTRODUCTORY. 29 

put a sufficient difficulty in the way. The co-operative body 
got tired of getting funds from and lending name to persons 
who had little or no science, and wanted F.R.S. to be in 
every case a Fellow Really Scientific. Accordingly, the num- 
ber of yearly elections was limited to fifteen recommended 
by the Council, unless the general body should choose to 
elect more; which it does not do. The election is now a 
competitive examination : it is no longer Are you able and 
willing to promote natural knowledge; it is Are you one 
of the upper fifteen of those who make such claim. In the 
list of candidates a list rapidly growing in number each 
year shows from thirty to forty of those whom Newton and 
Boyle would have gladly welcomed as fellow-laborers. And 
though the rejected of one year may be the accepted of the 
next or of the next but one, or but two, if self-respect will 
permit the candidate to hang on yet the time is clearly com- 
ing when many of those who ought to be welcomed will be 
excluded for life, or else shelved at last, when past work, 
with a scientific peerage. Coupled with this attempt to 
create a kind of order of knighthood is an absurdity so glar- 
ing that it should always be kept before the general eye. 
This distinction, this mark set by science upon successful 
investigation, is of necessity a class-distinction. Rowan 
Hamilton, one of the greatest names of our day in mathe- 
matical science, never could attach F.R.S. to his name he 
could not afford it. There is a condition precedent Four 
Red Sovereigns. It is four pounds a year, or to those who 
have contributed to the Transactions forty pounds down. 
This is as it should be: the Society must be supported. 
But it is not as it should be that a kind of title of honor 
should be forged, that a body should take upon itself to 
confer distinctions for science, when it is in the background 
and kept there when the distinction is trumpeted that 
the wearer is a man who can spare four pounds a year. I 
am well aware that in England a person who is not gifted 
either by nature or art, with this amount of money power, 



30 A BUDGET OF PARADOXES. 

is, with the mass, a very second-rate sort of Newton, what- 
ever he may be in the field of investigation. Even men of 
science, so called, have this feeling. I know that the scien- 
tific advisers of the Admiralty, who, years ago, received 
100 pounds a year each for his trouble, were sneered at by 
a wealthy pretender as "fellows to whom a hundred a year 
is an object." Dr. Thomas Young was one of them. To 
a bookish man I mean a man who can manage to collect 
books there is no tax. To myself, for example, 40 pounds 
worth of books deducted from my shelves, and the life-use 
of the Society's splendid library instead, would have been a 
capital exchange. But there may be, and are, men who want 
books, and cannot pay the Society's price. The Council 
would be very liberal in allowing books to be consulted. 
I have no doubt that if a known investigator were to call 
and ask to look at certain books, the Assistant-Secretary 
would forthwith seat him with the books before him, ab- 
sence of F.R.S. not in any wise withstanding. But this is 
not like having the right to consult any book on any day, 
and to take it away, if farther wanted. 

So much for the Royal Society as concerns myself. I 
must add that there is not a spark of party feeling against 
those who wilfully remain outside. The better minds of 
course know better; and the smaller savants look compla- 
cently on the idea of an outer world which makes elite of 
them. I have done such a thing as serve on a committee 
of the Society, and report on a paper: they had the sense 
to ask, and I had the sense to see that none of my opinions 
were compromised by compliance. And I will be of any 
use which does not involve the status of homo trium lite- 
rarum; as I have elsewhere explained, I would gladly be 
Fautor Realis Scientice, but I would not be taken for Falsa 
Rationis Sacerdos. 

Nothing worse will ever happen to me than the smile 
which individuals bestow on a man who does not groove. 
Wisdom, like religion, belongs to majorities ; who can won- 



INTRODUCTORY. 31 

der that it should be so thought, when it is so clearly pictured 
in the New Testament from one end to the other? 

The counterpart of paradox, the isolated opinion of one 
or of few, is the general opinion held by all the rest ; and the 
counterpart of false and absurd paradox is what is called the 
"vulgar error," the pseudodox. There is one great work on 
this last subject, the Pseudodoxia Epidemica of Sir Thomas 
Browne, the famous author of the Rellgio Medici ; it usually 
goes by the name of Browne "On Vulgar Errors" ( 1st ed. 
1646; 6th, 1672). A careful analysis of this work would 
show that vulgar errors are frequently opposed by scientific 
errors ; but good sense is always good sense, and Browne's 
book has a vast quantity of it. 

As an example of bad philosophy brought against bad 
observation. The Amphisbsena serpent was supposed to 
have two heads, one at each end; partly from its shape, 
partly because it runs backwards as well as forwards. On 
this Sir Thomas Browne makes the following remarks: 

"And were there any such species or natural kind of 
animal, it would be hard to make good those six positions 
of body which, according to the three dimensions, are as- 
cribed unto every Animal ; that is, infra, supra, ante, retro, 
dextrosum, sinistrosum: for if (as it is determined) that be 
the anterior and upper part wherein the senses are placed, 
and that the posterior and lower part which is opposite 
thereunto, there is no inferior or former part in this Animal ; 
for the senses, being placed at both extreams, doth make 
both ends anterior, which is impossible ; the terms being 
Relative, which mutually subsist, and are not without each 
other. And therefore this duplicity was ill contrived to place 
one head at both extreams, and had been more tolerable to 
have settled three or four at one. And therefore also Poets 
have been more reasonable than Philosophers, and Geryon 
or Cerberus less monstrous than Amphisbana" 



32 A BUDGET OF PARADOXES. 

There may be paradox upon paradox: and there is a 
good instance in the eighth century in the case of Virgil, 
an Irishman, Bishop of Salzburg and afterwards Saint, and 
his quarrels with Boniface, an Englishman, Archbishop of 
Mentz, also afterwards Saint. All we know about the matter 
is, that there exists a letter of 748 from Pope Zachary, citing 
Virgil then, it seems, at most a simple priest, though the 
Pope was not sure even of that to Rome to answer the 
charge of maintaining that there is another world (mundus) 
under our earth (terra), with another sun and another 
moon. Nothing more is known : the letter contains threats 
in the event of the charge being true; and there history 
drops the matter. Since Virgil was afterwards a Bishop 
and a Saint, we may fairly conclude that he died in the full 
flower of his orthodox reputation. It has been supposed 
and it seems probable that Virgil maintained that the earth 
is peopled all the way round, so that under some spots there 
are antipodes ; that his contemporaries, with very dim ideas 
about the roundness of the earth, and most of them with 
none at all, interpreted him as putting another earth under 
ours turned the other way, probably, like the second piece 
of bread-and-butter in a sandwich, with a sun and moon 
of its own. In the eighth century this would infallibly have 
led to an underground Gospel, an underground Pope, and 
an underground Avignon for him to live in. When, in later 
times, the idea of inhabitants for the planets was started, it 
was immediately asked whether they had sinned, whether 
Jesus Christ died for them, whether their wine and their 
water could be lawfully used in the sacraments, etc. 

On so small a basis as the above has been constructed a 
companion case to the persecution of Galileo. On one side 
the positive assertion, with indignant comment, that Virgil 
was deposed for antipodal heresy, on the other, serious at- 
tempts at justification, palliation, or mystification. Some 
writers say that Virgil was found guilty ; others that he gave 
satisfactory explanation, and became very good friends with 



INTRODUCTORY. 33 

Boniface: for all which see Bayle. Some have maintained 
that the antipodist was a different person from the canon- 
ized bishop : there is a second Virgil, made to order. When 
your shoes pinch, and will not stretch, always throw them 
away and get another pair : the same with your facts. Ba- 
ronius was not up to the plan of a substitute : his commen- 
tator Pagi (probably writing about 1690) argues for it in 
a manner which I think Baronius would not have approved. 
This Virgil was perhaps a slippery fellow. The Pope says 
he hears that Virgil pretended licence from him to claim 
one of some new bishoprics : this he declares is totally false. 
It is part of the argument that such a man as this could not 
have been created a Bishop and a Saint : on this point there 
will be opinions and opinions. 1 

Lactantius, four centuries before, had laughed at the an- 
tipodes in a manner which seems to be ridicule thrown on 
the idea of the earth's roundness. Ptolemy, without refer- 
ence to the antipodes, describes the extent of the inhabited 
part of the globe in a way which shows that he could have 
had no objection to men turned opposite ways. Probably, 
in the eighth century, the roundness of the earth was matter 
of thought only to astronomers. It should always be re- 
membered, especially by those who affirm persecution of a 
true opinion, that but for our knowing from Lactantius that 
the antipodal notion had been matter of assertion and denial 
among theologians, we could never have had any great con- 
fidence in Virgil really having maintained the simple theory 
of the existence of antipodes. And even now we are not 
entitled to affirm it as having historical proof : the evidence 

1 An Irish antiquary informs me that Virgil is mentioned in an- 
nals, at A. D. 784, as "Verghil, i. e., the geometer, Abbot of Achadhbo 
[and Bishop of Saltzburg] died in Germany in the thirteenth year of 
his bishoprick." No allusion is made to his opinions ; but it seems he 
was, by tradition, a mathematician. The Abbot of Aghabo (Queen's 
County) was canonized by Gregory IX, in 1233. The story of the 
second, or scapegoat, Virgil would be much damaged by the char- 
acter given to the real bishop, if there were anything in it to dilapi- 
date. A. De M. 



34 A BUDGET OF PARADOXES. 

goes to Virgil having been charged with very absurd notions, 
which it seems more likely than not were the absurd con- 
structions which ignorant contemporaries put upon sensible 
opinions of his. 

One curious part of this discussion is that neither side 
has allowed Pope Zachary to produce evidence to character. 
He shall have been an Urban, say the astronomers ; an Ur- 
ban he ought to have been, say the theologians. What sort 
of man was Zachary? He was eminently sensible and con- 
ciliatory; he contrived to make northern barbarians hear 
reason in a way which puts him high among that section of 
the early popes who had the knack of managing uneducated 
swordsmen. He kept the peace in Italy to an extent which 
historians mention with admiration. Even Bale, that Maha- 
rajah of pope-haters, allows himself to quote in favor of 
Zachary, that "multa Papalem dignitatem decentia, eadem- 
que prseclara (scilicet) opera confecit." 1 And this, though so 
willing to find fault that, speaking of Zachary putting a 
little geographical description of the earth on the portico of 
the Lateran Church, he insinuates that it was intended to 
affirm that the Pope was lord of the whole. Nor can he 
say how long Zachary held the see, except by announcing 
his death in 752, "cum decem annis pestilentiae sedi prae- 
fuisset." 2 

There was another quarrel between Virgil and Boni- 
face which is -an illustration. An ignorant priest had bap- 
tized "in nomine Patria, et Filia et Spirituo Sancto." Boni- 
face declared the rite null and void: Virgil maintained 
the contrary; and Zachary decided in favor of Virgil, on 
the ground that the absurd form was only ignorance of 
Latin, and not heresy. It is hard to believe that this man 
deposed a priest for asserting the whole globe to be in- 
habited. To me the little information that we have seems 

1 "He performed many acts befitting the Papal dignity, and like- 
wise many excellent (to be sure!) works." 

2 "After having been on the throne during ten years of p6tilence." 



INTRODUCTORY. 



35 



to indicate but not with certainty that Virgil maintained 
the antipodes: that his ignorant contemporaries travestied 
his theory into that of an underground cosmos; that the 
Pope cited him to Rome to explain his system, which, as 
reported, looked like what all would then have affirmed to 
be heresy; that he gave satisfactory explanations, and was 
dismissed with honor. It may be that the educated Greek 
monk, Zachary, knew his Ptolemy well enough to guess 
what the asserted heretic would say ; we have seen that he 
seems to have patronized geography. The description of the 
earth, according to historians, was a map ; this Pope may 
have been more ready than another to prick up his ears at 
any rumor of geographical heresy, from hope of informa- 
tion. And Virgil, who may have entered the sacred pres- 
ence as frightened as Jacquard, when Napoleon I sent for 
him and said, with a stern voice and threatening gesture, 
"You are the man who can tie a knot in a stretched string," 
may have departed as well pleased as Jacquard with the 
riband and pension which the interview was worth to him. 

A word more about Baronius. If he had been pope, as 
he would have been but for the opposition of the Spaniards, 
and if he had lived ten years longer than he did, and if 
Clavius, who would have been his astronomical adviser, had 
lived five years longer than he did, it is probable, nay almost 
certain, that the great exhibition, the proceeding against 
Galileo, would not have furnished a joke against theology 
in all time to come. For Baronius was sensible and witty 
enough to say that in the Scriptures the Holy Spirit intended 
to teach how to go to Heaven, not how Heaven goes ; and 
Clavius, in his last years, confessed that the whole system 
of the heavens had broken down, and must be mended. 

The manner in which the Galileo case, a reality, and the 
Virgil case, a fiction, have been hawked against the Roman 
see are enough to show that the Pope and his adherents 
have not cared much about physical philosophy. In truth, 
orthodoxy has always had other fish to fry. Physics, which 



36 A BUDGET OF PARADOXES. 

in modern times has almost usurped the name philosophy, in 
England at least, has felt a little disposed to clothe herself 
with all the honors of persecution which belong to the real 
owner of the name. But the bishops, etc. of the Middle 
Ages knew that the contest between nominalism and real- 
ism, for instance, had a hundred times more bearing upon 
orthodoxy than anything in astronomy, etc. A wrong notion 
about substance might play the mischief with transubstan- 
tiation. 

The question of the earth's motion was the single point 
in which orthodoxy came into real contact with science. 
Many students of physics were suspected of magic, many of 
atheism: but, stupid as the mistake may have been, it was 
bona fide the magic or the atheism, not the physics, which 
was assailed. In the astronomical case it was the very doc- 
trine, as a doctrine, independently of consequences, which 
was the corpus delicti: and this because it contradicted the 
Bible. And so it did; for the stability of the earth is as 
clearly assumed from one end of the Old Testament to 
the other as the solidity of iron. Those who take the 
Bible to be totidem verbis dictated by the God of Truth 
can refuse to believe it; and they make strange reasons. 
They undertake, a priori, to settle Divine intentions. The 
Holy Spirit did not mean to teach natural philosophy: this 
they know beforehand; or else they infer it from finding 
that the earth does move, and the Bible says it does not. 
Of course, ignorance apart, every word is truth, or the 
writer did not mean truth. But this puts the whole book on 
its trial: for we never can find out what the writer meant, 
until we otherwise find out what is true. Those who like 
may, of course, declare for an inspiration over which they 
are to be viceroys ; but common sense will either accept 
verbal meaning or deny verbal inspiration. 



A BUDGET OF PARADOXES. 

VOLUME I. 

THE STORY OF BURIDAN'S ASS. 
Questiones Morales, folio, 1489 [Paris]. By T. Buridan. 

This is the title from the Hartwell Catalogue of Law 
Books. I suppose it is what is elsewhere called the "Com- 
mentary on the Ethics of Aristotle," printed in 1489. 1 Buri- 
dan 2 (died about 1358) is the creator of the famous ass 
which, as Burdin's 3 ass, was current in Burgundy, perhaps 
is, as a vulgar proverb. Spinoza 4 says it was a jenny ass, 
and that a man would not have been so foolish ; but whether 
the compliment is paid to human or to masculine character 
does not appear perhaps to both in one. The story told 
about the famous paradox is very curious. The Queen of 
France, Joanna or Jeanne, was in the habit of sewing her 
Movers up in sacks, and throwing them into the Seine; not 
for blabbing, but that they might not blab certainly the 
safer plan. Buridan was exempted, and, in gratitude, in- 
vented the sophism. What it has to do with the matter 

J The work is the Questiones foannis Buridani super X libros Aris- 
totelis ad Nicomachum, curante Egidio Delfo. . . .Parisiis, 1489, folio. 
It also appeared at Paris in editions of 1499, 1513, and 1518, and at 
Oxford in 1637. 

2 Jean Buridan was born at Bethune about 1298, and died at Paris 
about 1358. He was professor of philosophy at the University of 
Paris and several times held the office of Rector. As a philosopher 
he was classed among the nominalists. 

8 So in the original. 

4 Baruch Spinoza, or Benedict de Spinoza as he later called himself, 
the pantheistic philosopher, excommunicated from the Jewish faith 
for heresy, was born at Amsterdam in 1632 and died there in 1677. 



38 A BUDGET OF PARADOXES. 

has never been explained. Assuredly qui facit per alium 
facit per se will convict Buridan of prating. The argument 
is as follows, and is seldom told in full. Buridan was for 
free-will that is, will which determines conduct, let mo- 
tives be ever so evenly balanced. An ass is equally pressed 
by hunger and by thirst ; a bundle of hay is on one side, a 
pail of water on the other. Surely, you will say, he will not 
be ass enough to die for want of food or drink ; he will then 
make a choice that is, will choose between alternatives of 
equal force. The problem became famous in the schools ; 
some allowed the poor donkey to die of indecision ; some 
denied the possibility of the balance, which was no answer 
at all. 

MICHAEL SCOTT'S DEVILS. 

The following question is more difficult, and involves 
free-will to all who answer "Which you please." If the 
northern hemisphere were land, and all the southern hemi- 
sphere water, ought we to call the northern hemisphere an 
island, or the southern hemisphere a lake? Both the ques- 
tions would be good exercises for paradoxers who must be 
kept employed, like Michael Scott's 1 devils. The wizard 

^Michael Scott, or Scot, was born about 1190, probably in Fife- 
shire, Scotland, and died about 1291. He was one of the best known 
savants of the court of Emperor Frederick II, and wrote upon astrol- 
ogy, alchemy, and the occult sciences. He was looked upon as a great 
magician and is mentioned among the wizards in Dante's Inferno. 

"That other, round the loins 
So slender of his shape, was Michael Scot, 
Practised in every slight of magic wile." Inferno, XX. 

Boccaccio also speaks of him : "It is not long since there was in 
this city (Florence) a great master in .necromancy, who was called 
Michele Scotto, because he was a Scot." Decameron, Dec. Giorno. 

Scott's mention of him in Canto Second of his Lay of the Last 
Minstrel, is well known : 

"In these fair climes, it was my lot 
To meet the wondrous Michael Scott ; 

A wizard of such dreaded fame, 
That when, in Salamanca's cave, 
Him listed his magic wand to wave, 

The bells would ring in Notre Dame!" 
Sir Walter's notes upon him are of interest. 



MICHAEL SCOTT'S DEVILS. 39 

knew nothing about squaring the circle, etc., so he set them 
to make ropes out of sea sand, which puzzled them. Stupid 
devils ; much of our glass is sea sand, and it makes beautiful 
thread. Had Michael set them to square the circle or to 
find a perpetual motion, he would have done his work much 
better. But all this is conjecture: who knows that I have 
not hit on the very plan he adopted? Perhaps the whole 
race of paradoxers on hopeless subjects are Michael's sub- 
ordinates, condemned to transmigration after transmigra- 
tion, until their task is done. 

The above was not a bad guess. A little after the time 
when the famous Pascal papers 2 were produced, I came into 
possession of a correspondence which, but for these papers, 
I should have held too incredible to be put before the world. 
But when one sheep leaps the ditch, another will follow: 
so I gave the following account in the Athenceum of Oc- 
tober 5, 1867: 

"The recorded story is that Michael Scott, being bound by 
contract to produce perpetual employment for a number of 
young demons, was worried out of his life in inventing 
jobs for them, until at last he set them to make ropes out of 
sea sand, which they never could do. We have obtained a 
very curious correspondence between the wizard Michael 
and his demon-slaves ; but we do not feel at liberty to say 
how it came into our hands. We much regret that we did 
not receive it in time for the British Association. It appears 
that the story, true as far as it goes, was never finished. 
The demons easily conquered the rope difficulty, by the 
simple process of making the sand into glass, and spinning 
the glass into thread, which they twisted. Michael, thor- 
oughly disconcerted, hit upon the plan of setting some to 

'These were some of the forgeries which Michel Chasles (1793- 
1880) was duped into buying. They purported to be a correspondence 
between Pascal and Newton and to show that the former had antici- 
pated some of the discoveries of the great English physicist and 
mathematician. That they were forgeries was shown by Sir David 
Brewster in 1855. 



40 A BUDGET OF PARADOXES. 

square the circle, others to find the perpetual motion, etc. 
He commanded each of them to transmigrate from one hu- 
man body into another, until their tasks were done. This 
explains the whole succession of cyclometers, and all the 
heroes of the Budget. Some of this correspondence is very 
recent; it is much blotted, and we are not quite sure of its 
meaning: it is full of figurative allusions to driving some- 
thing illegible down a steep into the sea. It looks like a 
humble petition to be allowed some diversion in the inter- 
vals of transmigration ; and the answer is 
Rumpat et serpens iter institutum, 3 

a line of Horace, which the demons interpret as a direction 
to come athwart the proceedings of the Institute by a sly 
trick. Until we saw this, we were suspicious of M. Libri. 4 
the unvarying blunders of the correspondence look like 
knowledge. To be always out of the road requires a map : 
genuine ignorance occasionally lapses into truth. We thought 
it possible M. Libri might have played the trick to show how 
easily the French are deceived ; but with our present in- 
formation, our minds are at rest on the subject. We see M. 
Chasles does not like to avow the real source of informa- 
tion: he will not confess himself a spiritualist." 

PHILO OF GADARA. 
Philo of Gadara 1 is asserted by Montucla, 2 on the author- 

8 "Let the serpent also break from its appointed path." 
*Guglielmo Brutus Icilius Timoleon Libri-Carucci della Som- 
maja, born at Florence in 1803; died at Fiesole in 1869. His His- 
toire des Sciences Mathematiques appeared at Paris in 1838, the en- 
tire first edition of volume I, save some half dozen that he had car- 
ried home, being burned on the day that the printing was completed. 
He was a great collector of early printed works on mathematics, 
and was accused of having stolen large numbers of them from other 
libraries. This accusation took him to London, where he bitterly 
attacked his accusers. There were two auction sales of his library, 
and a number of his books found their way into De Morgan's col- 
lection. 

1 Philo of Gadara lived in the second century B. C. He was a 
pupil of Sporus, who worked on the problem of the two mean pro- 
portionals. 

2 In his Histoire des Mathematiques, the first edition of which 



PHILO OF GADARA. 41 

ity of Eutocitis, 3 the commentator on Archimedes, to have 
squared the circle within the ten-thousandth part of a unit, 
that is, to four places of decimals. A modern classical dic- 
tionary represents it as done by Philo to ten thousand places 
of decimals. Lacroix comments on Montucla to the effect that 
myriad (in Greek ten thousand} is here used as we use it, 
vaguely, for an immense number. On looking into Eutocius, 
I find that not one definite word is said about the extent to 
which Philo carried the matter. I give a translation of the 
passage : 

"We ought to know that Apollonius Pergseus, in his 
Ocytocium [this work is lost], demonstrated the same by 
other numbers, and came nearer, which seems more accurate, 
but has nothing to do with Archimedes ; for, as before said, 
he aimed only at going near enough for the wants of life. 
Neither is Porus of Nicaea fair when he takes Archimedes 
to task for not giving a line accurately equal to the circum- 
ference. He says in his Cerii that his teacher, Philo of 
Gadara, had given a more accurate approximation (cts d*/Di- 
jSeo-repov? api.6fjiov<s dyayeiv) than that of Archimedes, or than 
7 to 22. But all these [the rest as well as Philo] miss the 
intention. They multiply and divide by tens of thousands, 
which no one can easily do, unless he be versed in the 
logistics [fractional computation] of Magnus [now un- 
known]." 

Montucla, or his source, ought not to have made this 
mistake. He had been at the Greek to correct Philo Gade- 
tanus, as he had often been called, and he had brought away 

appeared in 1758. Jean Etienne Montucla was born at Lyons in 
1725 and died at Versailles in 1799. He was therefore only thirty- 
three years old when his great work appeared. The second edition, 
with additions by D'Alembert, appeared in 1799-1802. He also wrote 
a work on the quadrature of the circle, Histoire des recherches sur 
la Quadrature du Cercle, which appeared in 1754. 

8 Eutocius of Ascalon was born in 480 A. D. He wrote com- 
mentaries on the first four books of the conies of Apollonius of 
Perga (247-222 B.C.). He also wrote on the Sphere and Cylinder 
and the Quadrature of the Circle, and on the two books on Equilib- 
rium of Archimedes (287-212 B. C.) 



42 A BUDGET OF PARADOXES. 

and quoted d TdSapw. Had he read two sentences further, 
he would have found the mistake. 

We here detect a person quite unnoticed hitherto by the 
moderns, Magnus the arithmetician. The phrase is, ironical; 
it is as if we should say, "To do this a man must be deep 
in Cocker." 4 Accordingly, Magnus, Baveme, 5 and Cocker, 
are three personifications of arithmetic; and there may be 
more. 

ON SQUARING THE CIRCLE. 

Aristotle, treating of the category of relation, denies that 
the quadrature has been found, but appears to assume that 
it can be done. Boethius, 1 in his comment on the passage, 
says that it has been done since Aristotle, but that the demon- 
stration is too long for him to give. Those who have no 
notion of the quadrature question may look at the English 
Cyclopcedia, art. "Quadrature of the Circle." 

Tetragonismus. Id est circuli quadratura per Campanum, Archi- 
medem Syracusanum, atque Boetium mathematical perspica- 
cissimos adinventa. At the end, Impressum Venetiis per loan. 
Bapti. Sessa. Anno ab incarnatione Domini, 1503. Die 28 
Augusti. 

* Edward Cocker was born in 1631 and died between 1671 and 
1677. His famous arithmetic appeared in 1677 and went through 
many editions. It was written in a style that appealed to teachers, 
and was so popular that the expression "According to Cocker" be- 
came a household phrase. Early in the nineteenth century there was 
a similar saying in America, "According to Daboll," whose arith- 
metic had some points of analogy to that of Cocker. Each had a 
well-known prototype in the ancient saying, "He reckons like Nico- 
machus of Gerasa." 

8 So in the original, for Barreme. Frangois Barreme was to 
France what Cocker was to England. He was born at Lyons in 
1640, and died at Paris in 1703. He published several arithmetics, 
dedicating them to his patron, Colbert. One of the best known of 
his works is Uarithmetique, ou le livre facile pour apprendre farith- 
metique soi-meme, 1677. The French word bareme or barreme, a 
ready-reckoner, is derived from his name. 

1 Born at Rome, about 480 A. D. ; died at Pavia, 524. Gibbon 
speaks of him as "the last of the Romans whom Cato or Tully could 
have acknowledged for their countryman." His works on arithmetic, 
music, and geometry were classics in the medieval schools. 



ON SQUARING THE CIRCLE. 43 

This book has never been noticed in the history of the 
subject, and I cannot find any mention of it. The quadrature 
of Campanus 2 takes the ratio of Archimedes, 3 7 to 22 to be 
absolutely correct; the account given of Archimedes is not 
a translation of his book ; and that of Boetius has more than 
is in Boet/nus. This book must stand, with the next, as the 
earliest in print on the subject, until further showing: Mur- 
hard 4 and Kastner 5 have nothing so early. It is edited by 
Lucas Gauricus, 6 who has given a short preface. Luca Gau- 
rico, Bishop of Civita Ducale, an astrologer of astrologers, 
published this work at about thirty years of age, and lived 
to eighty-two. His works are collected in folios, but I do 
not know whether they contain this production. The poor 
fellow could never tell his own fortune, because his father 
neglected to note the hour and minute of his birth. But if 
there had been anything in astrology, he could have worked 
back, as Adams 7 and Leverrier 8 did when they caught Nep- 

a Johannes Campanus, of Novarra, was chaplain to Pope Urban 
IV (1261-1264). He was one of the early medieval translators of 
Euclid from the Arabic into Latin, and the first printed edition of 
the Elements (Venice, 1482) was from his translation. In this work 
he probably depended not a little upon at least two or three earlier 
scholars. He also wrote De computo ecclesiastico Calendarium, and 
De quadratura circuit. 

8 Archimedes gave 3Vr and 3 10 Ai as the limits of the ratio of the 
circumference to the diameter of a circle. 

*Friedrich W. A. Murhard was born at Cassel in 1779 and died 
there in 1853. His Bibliotheca Mat hematic a, Leipsic, 1797-1805, is 
ill arranged and inaccurate, but it is still a helpful bibliography. De 
Morgan speaks somewhere of his indebtedness to it. 

B Abraham Gotthelf Kastner was born at Leipsic in 1719, and 
died at Gottingen in 1800. He was professor of mathematics and 
physics at Gottingen. His Geschichte der Mathematik (1796-1800) 
was a work of considerable merit. In the text of the Budget of 
Paradoxes the name appears throughout as Kastner instead of Kast- 
ner. 

6 Lucas Gauricus, or Luca Gaurico, born at Giffoni, near Naples, 
in 1476; died at Rome in 1558. He was an astrologer and mathe- 
matician, and was professor of mathematics at Ferrara in I53 1 * I n 
1545 he became bishop of Civita Ducale. 

T John Couch Adams was born at Lidcot, Cornwall, in 1819, and 
died in 1892. He and Leverrier predicted the discovery of Neptune 
from the perturbations in Uranus. 

8 Urbain- Jean- Joseph Leverrier was born at Saint-L6, Manche, 



44 A BUDGET OF PARADOXES. 

tune: at sixty he could have examined every minute of his 
day of birth, by the events of his life, and so would have 
found the right minute. He could then have gone on, by 
rules of prophecy. Gauricus was the mathematical teacher 
of Joseph Scaliger, 9 who did him no credit, as we shall see. 

BOVILLUS ON THE QUADRATURE PROBLEM. 

In hoc opere contenta Epitome Liber de quadratura Circuli. 

.... Paris, 1503, folio. 

The quadrator is Charles Bovillus, 1 who adopted the views 
of Cardinal Cusa, 2 presently mentioned. Montucla is hard 
on his compatriot, who, he says, was only saved from the 
laughter of geometers by his obscurity. Persons must guard 
against most historians of mathematics in one point: they 
frequently attribute to his own age the obscurity which a 
writer has in their own time. This tract was printed by 
Henry Stephens, 3 at the instigation of Faber Stapulensis, 4 

in 1811, and died at Paris in 1877. It was his data respecting the 
perturbations of Uranus that were used by Adams and himself in 
locating Neptune. 

* Joseph-Juste Scaliger, the celebrated philologist, was born at 
Agen in 1540, and died at Ley den in 1609. His Cyclometrica ele- 
menta, to which De Morgan refers, appeared at Leyden in 1594. 

1 The title is: In hoc libro contenta. . . .Introductio i geometria 
. . . .Liber de quadratura cirfuli. Liber de cubicatione sphere. Per- 
spectiva introductio. Carolus Bovillus, or Charles Bouvelles (Boii- 
elles, Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, 
and died at Noyon about 1533. He was canon and professor of 
theology at Noyon. His Introductio contains considerable work on 
star polygons, a favorite study in the Middle Ages and early Re- 
naissance. His work Que hoc volumine continetur. Liber de in- 
tellectu. Liber de sensu, etc., appeared at Paris in 1509-10. 

2 Nicolaus Cusanus, Nicolaus Chrypffs or Krebs, was born at 
Kues on the Mosel in 1401, and died at Todi, Umbria, August n, 
1464. He held positions of honor in the church, including the 
bishopric of Brescia. He was made a cardinal in 1448. He wrote 
several works on mathematics, his Opuscula varia appearing about 
1490, probably at Strasburg, but published without date or place. 
His Opera appeared at Paris in 1511 and again in 1514, and at Basel 
in 1565. 

"Henry Stephens (born at Paris about 1528, died at Lyons in 
1598) was one of the most successful printers of his day. He was 
known as Typographus Parisiensis, and to his press we owe some 
of the best works of the period.- 

4 Jacobus Faber Stapulensis (Jacques le Fevre d'Estaples) was 



BOVILLUS ON THE QUADRATURE PROBLEM. 45 

and is recorded by Dechales, 5 etc. It was also introduced into 
the Margarita Philosophica of 181 5, 6 in the same appendix 
with the new perspective from Viator. This is not extreme 
obscurity, by any means. The quadrature deserved it; but 
that is another point. 

It is stated by Montucla that Bovillus makes TT = V 10. 
But Montucla cites a work of 1507, Intro duct or ium Geo- 
metricum, which I have never seen. 7 He finds in it an 
account which Bovillus gives of the quadrature of the peas- 
ant laborer, and describes it as agreeing with his own. But 
the description makes TT = 3J, which it thus appears Bovillus 
could not distinguish from \/10. It seems also that this 3J, 
about which we shall see so much in the sequel, takes its rise 
in the thoughtful head of a poor laborer. It does him great 
honor, being so near the truth, and he having no means of 
instruction. In our day, when an ignorant person chooses 
to bring his fancy forward in opposition to demonstration 
which he will not study, he is deservedly laughed at. 

born at Estaples, near Amiens, in 1455, and died at Nerac in 1536. 
He was a priest, vicar of the bishop of Meaux, lecturer on philos- 
ophy at the College Lemoine in Paris, and tutor to Charles, son of 
Francois I. He wrote on philosophy, theology, and mathematics. 

8 Claude-Frangois Milliet de Challes was born at Chambery in 
1621, and died at Turin in 1678. He edited Eudidis Elementorum 
libri octo in 1660, and published a Cursus seu mundus mathematicus, 
which included a short history of mathematics, in 1674. He also 
wrote on mathematical geography. 

6 This date should be 1503, if he refers to the first edition. It is 
well known that this is the first encyclopedia worthy the name to 
appear in print. It was written by Gregorius Reisch (born at 
Balingen, and died at Freiburg in 1487), prior of the cloister at 
Freiburg and confessor to Maximilian I. The first edition appeared 
at Freiburg in 1503, and it passed through many editions in the 
sixteenth and seventeenth centuries. The title of the 1504 edition 
reads: Aepitoma omnis phylosophiae. alias Margarita phylosophica 
tractans de omni genere scibili : Cum additionibus : Quae in alijs non 
habentur. 

'This is the Introductio in arithmeticam Divi S. Boetii Eft- 
tome rerum geometricarum ex geometrica introductio C. Bovilli. 
De quadratura circuli demonstratio ex Campano, that appeared with- 
out date about 1507. 



46 A BUDGET OF PARADOXES. 

THE STORY OF LACOMME'S ATTEMPT AT QUADRA- 
TURE. 

Mr. James Smith, 1 of Liverpool hereinafter notorified 
attributes the first announcement of 3J to M. Joseph La- 
comme, a French well-sinker, of whom he gives the following 
account : 

"In the year 1836, at which time Lacomme could neither 
read nor write, he had constructed a circular reservoir and 
wished to know the quantity of stone that would be re- 
quired to pave the bottom, and for this purpose called on a 
professor of mathematics. On putting his question and giv- 
ing the diameter, he was surprised at getting the following 
answer from the Professor : 'Qu'il lui etait impossible de le 
lui dire au juste, attendu que personne n'avait encore pit 
trouver d'une maniere exacte le rapport de la cir -conference 
au diametre.' 2 From this he was led to attempt the solution 
of the problem. His first process was purely mechanical, 
and he was so far convinced he had made the discovery that 
he took to educating himself, and became an expert arith- 
metician, and then found that arithmetical results agreed 
with his mechanical experiments. He appears to have eked 
out a bare existence for many years by teaching arithmetic, 
all the time struggling to get a hearing from some of the 
learned societies, but without success. In the year 1855 he 
found his way to Paris, where, as if by accident, he made 
the acquaintance of a young gentleman, son of M. Winter, 
a commissioner of police, and taught him his peculiar meth- 
ods of calculation. The young man was so enchanted that 
he strongly recommended Lacomme to his father, and sub- 

1 Born at Liverpool in 1805, and died there about 1872. He was 
a merchant, and in 1865 he published, at Liverpool, a work entitled 
The Quadrature of the Circle, or the True Ratio between the Diam- 
eter and Circumference geometrically and mathematically demon- 
strated. In this he gives the ratio as exactly 3Vs. 

2 "That it would be impossible to tell him exactly, since no one 
had yet been able to find precisely the ratio of the circumference to 
the diameter." 



NICOLAUS OF CUSA'S ATTEMPT. 47 

sequently through M. Winter he obtained an introduction 
to the President of the Society of Arts and Sciences of Paris. 
A committee of the society was appointed to examine and 
report upon his discovery, and the society at its seance of 
March 17, 1856, awarded a silver medal of the first class to 
M. Joseph Lacomme for his discovery of the true ratio of 
diameter to circumference in a circle. He subsequently re- 
ceived three other medals from other societies. While writ- 
ing this I have his likeness before me, with his medals on 
his breast, which stands as a frontispiece to a short biography 
of this extraordinary man, for which I am indebted to the 
gentleman who did me the honor to publish a French trans- 
lation of the pamphlet I distributed at the meeting of the 
British Association for the Advancement of Science, at Ox- 
ford, in 1860. Correspondent, May 3, 1866. 

My inquiries show that the story of the medals is not 
incredible. There are at Paris little private societies which 
have not so much claim to be exponents of scientific opinion 
as our own Mechanics' Institutes. Some of them were in- 
tended to give a false lustre: as the "Institut Historique," 
the members of which are "Membre de ITnstitut Historique." 
That M. Lacomme should have got four medals from so- 
cieties of this class is very possible : that he should have re- 
ceived one from any society at Paris which has the least 
claim to give one is as yet simply incredible. 

NICOLAUS OF CUSA'S ATTEMPT. 
Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio. 

The real title is "Haec accurata recognitio trium volu- 
mimmi operum clariss. P. Nicolai Cusse . . . . proxime se- 
quens pagina monstrat." 1 Cardinal Cusa, who died in 1464, 
is one of the earliest modern attempters. His quadrature 
is found in the second volume, and is now quite unreadable. 

1 This is the Paris edition : "Parisiis : ex officina Ascensiana anno 

Christi MDXIIII," as appears by the colophon of the second 

volume to which De Morgan refers. 



48 A BUDGET OF PARADOXES. 

In these early days every quadrator found a geometrical 
opponent, who finished him. Regimontanus 2 did this office 
for the Cardinal. 

HENRY CORNELIUS AGRIPPA. 

De Occulta Philosophia libri III. By Henry Cornelius Agrippa. 

Lyons, 1550, 8vo. 
De incertitudine et vanitate scientiarum. By the same. Cologne. 

1531, 8vo. 

The first editions of these works were of 1530, as well 
as I can make out; but the first was in progress in 15 10. 1 
In the second work Agrippa repents of having wasted time 
on the magic of the first; but all those who actually deal 
with demons are destined to eternal fire with Jamnes and 
Mambres and Simon Magus. This means, as is the fact, 
that his occult philosophy did not actually enter upon black 
magic, but confined itself to the power of the stars, of num- 
bers, etc. The fourth book, which appeared after the death 
of Agrippa, and really concerns dealing with evil spirits, 
is undoubtedly spurious. It is very difficult to make out 
what Agrippa really believed on the subject. I have intro- 
duced his books as the most marked specimens of treatises 
on magic, a paradox of our day, though not far from ortho- 
doxy in his ; and here I should have ended my notice, if I 
had not casually found something more interesting to the 
reader of our day. 

2 Regiomontanus, or Johann Miiller of Konigsberg (Regiomon- 
tanus), was born at Konigsberg in Franconia, June 5, 1436, and died 
at Rome July 6, 1476. He studied at Vienna under the great astron- 
omer Peuerbach, and was his most famous pupil. He wrote numer- 
ous works, chiefly on astronomy. He is also known by the names 
loannes de Monte Regio, de Regiomonte, loannes Germanus de 
Regiomonte, etc. 

1 Henry Cornelius Agrippa was born at Cologne in 1486 and died 
either at Lyons in 1534 or at Grenoble in 1535. He was professor of 
theology at Cologne and also at Turin. After the publication of his 
De Occulta Philosophia he was imprisoned for sorcery. Both works 
appeared at Antwerp in 1530, and each passed through a large num- 
ber of editions. A French translation appeared in Paris in 1582, 
and an English one in London in 1651. 



.WHICH LEADS TO WALTER SCOTT. 49 



WHICH LEADS TO WALTER SCOTT. 

Walter Scott, it is well known, was curious on all matters 
connected with magic, and has used them very widely. But 
it is hardly known how much pains he has taken to be cor- 
rect, and to give the real thing. The most decided detail of 
a magical process which is found in his writings is that of 
Dousterswivel in The Antiquary, and it is obvious, by his 
accuracy of process, that he does not intend the adept for a 
mere impostor, but for one who had a lurking belief in the 
efficacy of his own processes, coupled with intent to make 
a fraudulent use of them. The materials for the process 
are taken from Agrippa. I first quote Mr. Dousterswivel: 

". . .1 take a silver plate when she [the moon] is in her 
fifteenth mansion, which mansion is in de head of Libra, and 
I engrave upon one side de worts Schedbarschemoth Schar- 
tachan [ch should be t] dat is, de Intelligence of de In- 
telligence of de moon and I make his picture like a flying 
serpent with a turkey-cock's head vary well Then upon 
this side I make de table of de moon, which is a square of 
nine, multiplied into itself, with eighty-one numbers [nine] 
on every side and diameter nine " 

In the De Occulta Philosophia, p. 290, we find that the 
fifteenth mansion of the moon incipit capite Libra, and is 
good pro extrahendis thesauris, the object being to discover 
hidden treasure. In p. 246, we learn that a silver plate must 
be used with the moon. In p. 248, we have the words which 
denote the Intelligence, etc. But, owing to the falling of a 
number into a wrong line, or the misplacement of a line, one 
or other which takes place in all the editions I have exam- 
ined Scott has, sad to say, got hold of the wrong words; 
he has written down the demon of the demons of the moon. 
Instead of the gibberish above, it should have been Malcha 
betarsisim hed beruah schenhakim. In p. 253, we have the 
magic square of the moon, with eighty-one numbers, and the 
symbol for the Intelligence, which Scott likens to a flying 



50 A BUDGET OF PARADOXES. 

serpent with a turkey-cock's head. He was obliged to say 
something; but I will stake my character and so save a 
woodcut on the scratches being more like a pair of legs, 
one shorter than the other, without a body, jumping over a 
six-barred gate placed side uppermost. Those who thought 
that Scott forged his own nonsense, will henceforth stand 
corrected. As to the spirit Peolphan, etc., no doubt Scott 
got it from the authors he elsewhere mentions, Nicolaus 
Remigius 1 and Petrus Thyracus; but this last word should 
be Thyrseus. 

The tendency of Scott's mind towards prophecy is very 
marked, and it is always fulfilled. Hyder, in his disguise, 
calls out to Tippoo : "Cursed is the prince who barters jus- 
tice for lust; he shall die in the gate by the sword of the 
stranger." Tippoo was killed in a gateway at Seringapatam. 2 

FINAEUS ON CIRCLE SQUARING. 
Orontii Finaei . . . Quadratura Circuli. Paris, 1544, 4to. 

Orontius 1 squared the circle out of all comprehension; 
but he was killed by a feather from his own wing. His 

1 Nicolaus Remegius was born in Lorraine in 1554, and died at 
Nancy in 1600. He was a jurist and historian, and held the office 
of procurator general to the Duke of Lorraine. 

2 This was at the storming of the city by trie British on May 4, 
1799. From his having been born in India, all this appealed strongly 
to the interests of De Morgan. 

1 Orontius Finaeus, or Oronce Fine, was born at Brianc.on in 1494 
and died at Paris, October 6, 1555. He was imprisoned by Frangois 
I for refusing to recognize the concordat (1517). He was made 
professor of mathematics in the College Royal (later called the 
College de France) in 1532. He wrote extensively on astronomy 
and geometry, but was by no means a great scholar. He was a 
pretentious man, and his works went through several editions. His 
Protomathesis appeared at Paris in 1530-32. The work referred to 
by De Morgan is the Quadratura clrculi tandem inventa & clarissime 

demonstrata Lutetiae Parisiorum, 1544, fol. In the 1556 edition 

of his De rebus mathematicis , hactenus desideratis, Libri IIII, pub- 
lished at Paris, the subtitle is: Quibus inter catera, Circuli quadra- 
tura Centum modis, & supra, per eundem Orontlum recenter ex- 
cogitatis, demonstrates, so that he kept up his efforts until his 
death. 



FINAEUS ON CIRCLE SQUARING. 51 

former pupil, John Buteo, 2 the same who I believe for the 
first time calculated the question of Noah's ark, as to its 
power to hold all the animals and stores, unsquared him 
completely. Orontius was the author of very many works, 
and died in 1555. Among the laudatory verses which, as 
was usual, precede this work, there is one of a rare charac- 
ter: a congratulatory ode to the wife of the author. The 
French now call this writer Oronce Finee; but there is 
much difficulty about delatinization. Is this more correct 
than Oronce Fine, which the translator of De Thou uses? 
Or than Horonce Phine, which older writers give ? I cannot 
understand why M. de Viette 3 should be called Viete, because 
his Latin name is Vieta. It is difficult to restore Buteo ; for 
not only now is butor a blockhead as well as a bird, but we 
really cannot know what kind of bird Buteo stood for. We 
may be sure that Madame Fine was Denise Blanche; for 
Dionysia Candida can mean nothing else. Let her shade 
rejoice in the fame which Hubertus Sussannaeus has given 
her. 

I ought to add that the quadrature of Orontius, and 
solutions of all the other difficulties, were first published in 
De Rebus Mathematicis Hactenus Desideratis* of which I 
have not the date. 

'Johannes Buteo (Boteo, Buteon, Bateon) was born in Dauphine 
c. 1485-1489, and died in a cloister in 1560 or 1564. Some writers 
give Charpey as the place and 1492 as the date of his birth, and 
state that he died at Canar in 1572. He belonged to the order of 
St. Anthony, and wrote chiefly on geometry, exposing the pretenses 
of Finaeus. His Opera geometrica appeared at Lyons in 1554, and 
his Logistica and De quadrature, circuit libri duo at Lyons in 1559. 

'This is the great French algebraist, Francois Viete (Vieta), 
who was born at Fontenay-le-Comte in 1540, and died at Paris, 
December 13, 1603. His well-known Isagoge in artem analyticam 
appeared at Tours in 1591. His Opera mathematica was edited by 
Van Schooten in 1646. 

4 This is the De Rebus mathematics hactenus desideratis, Libri 
IIII, that appeared in Paris in 1556. For the title page see Smith, 
D. K, Kara Arithmetica, Boston, 1908, p. 280. 



52 A BUDGET OF PARADOXES. 

DUCHESNE, AND A DISQUISITION ON ETYMOLOGY. 

Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomicum, 

id est, nova doctrina sinuum et triangulorum Strasburg, 

1588, 410. 1 

People choose the name of this astronomer for them- 
selves: I take Ursus, because he was a bear. This book 
gave the quadrature of Simon Duchesne, 2 or a Quercu, which 
excited Peter Metius, 3 as presently noticed. It also gave that 
unintelligible reference to Justus Byrgius which has been 
used in the discussion about the invention of logarithms. 4 

The real name of Duchesne is Van der Eycke. I have 
met with a tract in Dutch, Letterkundige Aanteekeningen, 
upon Van Eycke, Van Ceulen, 5 etc., by J.J. Dodt van Flens- 
burg, 6 which I make out to be since 1841 in date. I should 

*The title is correct except for a colon after Astronomicum. 
Nicolaus Raimarus Ursus was born in Henstede or Hattstede, in 
Dithmarschen, and died at Prague in 1599 or 1600. He was a pupil 
of Tycho Brahe. He also wrote De astronomis hypothesibus (1597) 
and Arithmetica analytica vulgo Cosa oder Algebra (1601).- 

2 Born at Dole, Franche-Comte, about 1550, died in Holland 
about 1600. The work to which reference is made is the Quadrature 
du cercle, ou maniere de trouver un quarre egal au cercle donne, 
which appeared at Delft in 1584. Duchesne had the courage of his 
convictions, not only on circle-squaring but on religion as well, for he 
was obliged to leave France because of his conversion to Calvinism. 
De Morgan's statement that his real name is Van der Eycke is 
curious, since he was French born. The Dutch may have translated 
his name when he became professor at Delft, but we might equally 
well say, that his real name was Quercetanus or a Quercu. 

'This was the father of Adriaan Metius (1571-1635). He was a 
mathematician and military engineer, and suggested the ratio "% 
for TT, a ratio afterwards published by his son. The ratio, then new 
to Europe, had long been known and used in China, having been 
found by Tsu Ch'ung-chih (428-499 A. D.). 

4 This was Jost Biirgi, or Justus Byrgius, the Swiss mathemati- 
cian of whom Kepler wrote in 1627: "Apices logistici Justo Byrgio 
multis annis ante editionem Neperianam viam prseiverunt ad hos 
ipsissimos logarithmos." He constructed a table of antilogarithms 
(Arithmetische und geometrische Progress-Tabulen), but it was not 
published until after Napier's work appeared. 

8 Ludolphus Van Ceulen, born at Hildesheim, and died at Leyden 
in 1610. It was he who first carried the computation of * to 35 deci- 
mal places. 

"Jens Jenssen Dodt, van Flensburg, a Dutch historian, who died 
in 1847. 



FALCO'S RARE TRACT. 53 

much like a translation of this tract to be printed, say in the 
Phil. Mag. Dutch would be clear English if it were prop- 
erly spelt. For example, learn-master would be seen at 
once to be teacher', but they will spell it leermeester. Of 
these they write as van deze\ widow the make weduwe. 
All this is plain to me, who never saw a Dutch dictionary in 
my life; but many of their misspellings are quite uncon- 
querable. 

FALCO'S RARE TRACT. 

Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli 
quadraturam invenit. Antwerp, 1589, 4to. 1 

The attempt is more than commonly worthless; but as 
Montucla and others have referred to the verses at the end, 
and as the tract is of the rarest, I will quote them: 

Circulus loquitur. 
Vocabar ante circulus 
Eramque curvus undique 
Ut alta sblis orbita 
Et arcus ille nubium. 
Eram figura nobilis 
Carensque sola origine 
Carensque sola termino. 
Modo indecora prodeo 
Novisque feeder angulis. 
Nee hoc peregit Archytas 2 
Neque Icari pater neque 
Tuus, lapete, films. 
Quis ergo casus aut Deus 
Meam quadravit aream? 

Responded auctor. 
Ad alta Turise ostia 
Lacumque limpidissimum 
Sita est beata civitas 

*I do not know this edition. There was one "Antverpiae apud 
Petrum Bellerum sub scuto Burgundiae," 4to, in 1591. 

2 Archytas of Tarentum (430-365 B.C.) who wrote on propor- 
tion, irrationals, and the duplication of the cube. 



54 A BUDGET OF PARADOXES. 

Parum Saguntus abfuit 
Abestque Sucro plusculum. 
Hie est poeta quispiam 
Libenter astra consulens 
Sibique semper arrogans 
Negata doctioribus, 
Senex ubique cogitans 
Sui frequenter immemor 
Nee explicare circinum 
Nee exarare lineas 
Sciens ut ipse prsedicat 
Hie ergo bellus artifex 
Tuam quadravit aream. 3 

Falco's verses are pretty, if the o - mysteries be correct ; 
but of these things I have forgotten what I knew. [One 
mistake has been pointed out to me: it is Archytas]. 

As a specimen of the way in which history is written, I 
copy the account which Montucla who is accurate when he 
writes about what he has seen gives of these verses. He 
gives the date 1587; he places the verses at the beginning 
instead of the end; he says the circle thanks its quadrator 
affectionately; and he says the good and modest chevalier 
gives all the glory to the patron saint of his order. All of 
little consequence, as it happens ; but writing at second-hand 
makes as complete mistakes about more important matters. 

8 The Circle Speaks. 

"At first a circle I was called, But now unlovely do I seem 

And was a curve around about Polluted by some angles new. 

Like lofty orbit of the sun This thing Archytas hath not done 

Or rainbowarch amongthe clouds. Nor noble sire of Icarus 

A noble figure then was I Nor son of thine, lapetus. 

And lacking nothing but a start, What accident or god can then 

And lacking nothing but an end. Have quadrated mine area?" 

The Author Replies. 

"By deepest mouth of Turia What is denied to wiser men; 

And lake of limpid clearness, lies An old man musing here and there 
A happy state not far removed And oft forgetful of himself, 
From old Saguntus ; farther yet Not knowing how to rightly place 
A little way from Sucro town. The compasses, nor draw a line, 
In this place doth a poet dwell, As he doth of himself relate. f 
Who oft the stars will closely scan, This craftsman fine, in sooth it is 
And always for himself doth claim Hath quadrated thine area." 



BUNGUS ON THE MYSTERY OF NUMBER. 55 



BUNGUS ON THE MYSTERY OF NUMBER. 

Petri Bungi Bergomatis Numerorum mysteria. Bergomi [Ber- 
gamo], 1591, 4to. Second Edition. 

The first edition is said to be of 1585 j 1 the third, Paris, 
1618. Bungus is not for my purpose on his own score, but 
those who gave the numbers their mysterious characters: 
he is but a collector. He quotes or uses 402 authors, as we 
are informed by his list ; this just beats Warburton, 2 whom 
some eulogist or satirist, I forget which, holds up as having 
used 400 authors in some one work. Bungus goes through 
1, 2, 3, etc., and gives the account of everything remarkable 
in which each number occurs ; his accounts not being always 
mysterious. The numbers which have nothing to say for 
themselves are omitted : thus there is a gap between 50 and 
60. In treating 666, Bungus, a good Catholic, could not 
compliment the Pope with it, but he fixes it on Martin 
Luther with a little forcing. If from A to I represent 1-10, 
from K to S 10-90, and from T to Z 100-500, we see: 

MARTIN LUTERA 
30 1 80 100 9 40 20 200 100 5 80 1 
which gives 666. Again, in Hebrew, Lulter does the same : 

i n 5 i 5 

200 400 30 6 30 

And thus two can play at any game. The second is better 
than the first : to Latinize the surname and not the Christian 

*Pietro Bongo, or Petrus Bungus, was born at Bergamo, and 
died there in 1601. His work on the Mystery of Numbers is one of 
the most exhaustive and erudite ones of the mystic writers. The 
first edition appeared at Bergamo in 1583-84; the second, at Ber- 
gamo in 1584-85; the third, at yenice in 1585; the fourth, at Ber- 
gamo in 1590; and the fifth, which De Morgan calls the second, in 
1591. Other editions, before the Paris edition to which he refers, 
appeared in 1509 and 1614; and the colophon of the Paris edition is 
dated 1617. See the editor's Rara Arithmetic^ pp. 380-383. 

* William Warburton (1698-1779), Bishop of Gloucester, whose 
works got him into numerous literary quarrels, being the subject of 
frequent satire. 



56 A BUDGET OF PARADOXES. 

name is very unscholarlike. The last number mentioned is a 
thousand millions ; all greater numbers are dismissed in half 
a page. Then follows an accurate distinction between num- 
ber and multitude a thing much wanted both in arithmetic 
and logic. 

WHICH LEADS TO A STORY ABOUT THE ROYAL SO- 
CIETY. 

What may be the use of such a book as this? The last 
occasion on which it was used was the following. Fifteen 
or sixteen years ago the Royal Society determined to restrict 
the number of yearly admissions to fifteen men of science, 
and noblemen ad libitum ; the men of science being selected 
and recommended by the Council, with a power, since prac- 
tically surrendered, to the Society to elect more. This plan 
appears to me to be directly against the spirit of their char- 
ter, the true intent of which is, that all who are fit should be 
allowed to promote natural knowledge in association, from 
and after the time at which they are both fit and willing. 
It is also working more absurdly from year to year; the 
tariff of fifteen per annum will soon amount to the practical 
exlusion of many who would be very useful. This begins 
to be felt already, I suspect. But, as appears above, the 
body of the Society has the remedy in its own hands. When 
the alteration was discussed by the Council, my friend the 
late Mr. Galloway, 1 then one of the body, opposed it strongly, 
and inquired particularly into the reason why -fifteen, of all 
numbers, was the one to be selected. Was it because fifteen 
is seven and eight, typifying the Old Testament Sabbath, 
and the New Testament day of the resurrection following? 
Was it because Paul strove fifteen days against Peter, prov- 
ing that he was a doctor both of the Old and New Testa- 
ment? Was it because the prophet Hosea bought a lady 

^Thomas Galloway (1796-1851), who was professor of mathe- 
matics at Sandhurst for a time, and was later the actuary of the 
Amicable Life Assurance Company of London. In the latter capac- 
ity he naturally came to be associated with De Morgan. 



A QUESTION OF EVIDENCE. 57 

for fifteen pieces of silver? Was it because, according to 
Micah, seven shepherds and eight chiefs should waste the 
Assyrians? Was it because Ecclesiastes commands equal 
reverence to be given to both Testaments such was the 
interpretation in the words "Give a portion to seven, and 
also to eight"? Was it because the waters of the Deluge 
rose fifteen cubits above the mountains? or because they 
lasted fifteen decades of days? Was it because Ezekiel's 
temple had fifteen steps? Was it because Jacob's ladder 
has been supposed to have had fifteen steps ? Was it because 
fifteen years were added to the life of Hezekiah? Was it 
because the feast of unleavened bread was on the fifteenth 
day of the month ? Was it because the scene of the Ascen- 
sion was fifteen stadia from Jerusalem? Was it because 
the stone-masons and porters employed in Solomon's temple 
amounted to fifteen myriads ? etc. The Council were amused 
and astounded by the volley of fifteens which was fired at 
them ; they knowing nothing about Bungus, of which Mr. 
Galloway who did not, as the French say, indicate his 
sources possessed the copy now before me. In giving this 
anecdote I give a specimen of the book, which is exceedingly 
rare. Should another edition ever appear, which is not very 
probable, he would be but a bungling Bungus who should 
forget the fifteen of the Royal Society. 

AND ALSO TO A QUESTION OF EVIDENCE. 

[I make a remark on the different colors which the same 
person gives to one story, according to the bias under which 
he tells it. My friend Galloway told me how he had quizzed 
the Council of the Royal Society, to my great amusement. 
Whenever I am struck by the words of any one, I carry 
away a vivid recollection of position, gestures, tones, etc. 
I do not know whether this be common or uncommon. I 
never recall this joke without seeing before me my friend, 
leaning against his bookcase, with Bungus open in his hand, 
and a certain half-depreciatory tone which he often used 



58 A BUDGET OF PARADOXES. 

when speaking of himself. Long after his death, an F.R.S. 
who was present at the discussion, told me the story. I did 
not say I had heard it, but I watched him, with Galloway 
at the bookcase before me. I wanted to see whether the two 
would agree as to the fact of an enormous budget of fifteens 
having been fired at the Council, and they did agree per- 
fectly. But when the paragraph of the Budget appeared in 
the Athenaum, my friend, who seemed rather to object to 
the showing-up, assured me that the thing was grossly ex- 
aggerated; there was indeed a fifteen or two, but nothing 
like the number I had given. I had, however, taken sharp 
note of the previous narration. 

AND TO ANOTHER QUESTION OF EVIDENCE. 

I will give another instance. An Indian officer gave me 
an account of an elephant, as follows. A detachment was 
on the march, and one of the gun-carriages got a wheel off 
the track, so that it was also off the ground, and hanging 
over a precipice. If the bullocks had moved a step, carriages, 
bullocks, and all must have been precipitated. No one knew 
what could be done until some one proposed to bring up an 
elephant, and let him manage it his own way. The elephant 
took a moment's survey of the fix, put his trunk under the 
axle of the free wheel, and waited. The surrounders, who 
saw what he meant, moved the bullocks gently forward, the 
elephant followed, supporting the axle, until there was 
ground under the wheel, when he let it quietly down. From 
all I had heard of the elephant, this was not too much to 
believe. But when, years afterwards, I reminded my friend 
of his story, he assured me that I had misunderstood him, 
that the elephant was directed to put his trunk under the 
wheel, and saw in a moment why. This is reasonable sagac- 
ity, and very likely the correct account ; but I am quite sure 
that, in the fit of elephant-worship under which the story 
was first told, it was told as I have first stated it.] 



GIORDANO BRUNO AND HIS PARADOXES. 59 



GIORDANO BRUNO AND HIS PARADOXES. 

[Jordani Bruni Nolani de Monade, Numero et Figura. . .item de 
Innumerabilibus, Immense, et Infigurabili.. .Frankfort, 1591, 
Svo. 1 

I cannot imagine how I came to omit a writer whom I 
have known so many years, unless the following story will 
explain it. The officer reproved the boatswain for perpetual 
swearing ; the boatswain answered that he heard the officers 
swear. "Only in an emergency," said the officer. "That's 
just it," replied the other; "a boatswain's life is a life of 
'mergency." Giordano Bruno was all paradox; and my 
mind was not alive to his paradoxes, just as my ears might 
have become dead to the boatswain's oaths. He was, as has 
been said, a vorticist before Descartes, 2 an optimist before 
Leibnitz, a Copernican before Galileo. It would be easy 
to collect a hundred strange opinions of his. He was born 
about 1550, and was roasted alive at Rome, February 17, 
1600, for the maintenance and defence of the holy Church, 
and the rights and liberties of the same. These last words 
are from the writ of our own good James I, under which 
Leggatt 3 was roasted at Smithfield, in March 1612; and if 
I had a copy of the instrument under which Wightman 4 was 
roasted at Lichfield, a month afterwards, I daresay I should 

1 Giordano Bruno was born near Naples about i55o ; He left the 
Dominican order to take up Calvinism, and among his publications 
was L' expulsion de la bete triomphante. He taught philosophy at 
Paris and Wittenberg, and some of his works were published in 
England in 1583-86. Whether or not he was roasted alive "for the 
maintenance and defence of the holy Church," as De Morgan states, 
depends upon one's religious point of view. At any rate, he was 
roasted as a heretic. 

2 Referring to part of his Discours de la methode, Leyden, 1637. 

'^Bartholomew Legate, who was born in Essex about 1575' He 
denied the divinity of Christ and was the last heretic burned at 
Smithfield. 

* Edward Wightman, born probably in Staffordshire. He was 
anti-Trinitarian, and claimed to be the Messiah. He was the last 
man burned for heresy in England. 



6Q A BUDGET OF PARADOXES. 

find something quite as edifying. I extract an account which 
I gave of Bruno in the Comp. Aim. for 1855: 

"He was first a Dominican priest, then a Calvinist; and 
was roasted alive at Rome, in 1600, for as many heresies of 
opinion, religious and philosophical, as ever lit one fire. 
Some defenders of the papal cause have at least worded 
their accusations so to be understood as imputing to him 
villainous actions. But it is positively certain that his death 
was due to opinions alone, and that retractation, even after 
sentence, would have saved him. There exists a remarkable 
letter, written from Rome on the very day of the murder, 
by Scioppius 5 (the celebrated scholar, a waspish convert from 
Lutheranism, known by his hatred to Protestants and Jes- 
uits) to Rittershusius, 6 a well-known Lutheran writer on 
civil and canon law, whose works are in the index of pro- 
hibited books. This letter has been reprinted by Libri (vol. 
iv. p. 407). The writer informs his friend (whom he wished 
to convince that even a Lutheran would have burnt Bruno) 
that all Rome would tell him that Bruno died for Lutheran- 
ism ; but this is because the Italians do not know the differ- 
ence between one heresy and another, in which simplicity 
(says the writer) may God preserve them. That is to say, 
they knew the difference between a live heretic and a roasted 
one by actual inspection, but had no idea of the difference 
between a Lutheran and a Calvinist. The countrymen of 
Boccaccio would have smiled at the idea which the German 
scholar entertained of them. They said Bruno was burnt 
for Lutheranism, a name under which they classed all Prot- 
estants : and they are better witnesses than Schopp, or Sciop- 
pius. He then proceeds to describe to his Protestant friend 
(to whom he would certainly not have omitted any act 
which both their churches would have condemned) the mass 
of opinions with which Bruno was charged; as that there 

5 Caspar ScHopp, born at Neumarck < in 1576, died at Padua in 
1649; grammarian, philologist, and satirist. 

6 Konrad Ritterhusius, born at Brunswick in 1560 ; died at Altdorf 
in 1613. He was a jurist of some power. 



GIORDANO BRUNO AND HIS PARADOXES. 61 

are innumerable worlds, that souls migrate, that Moses was 
a magician, that the Scriptures are a dream, that only the 
Hebrews descended from Adam and Eve, that the devils 
would be saved, that Christ was a magician and deservedly 
put to death, etc. In fact, says he, Bruno has advanced all 
that was ever brought forward by all heathen philosophers, 
and by all heretics, ancient and modern. A time for retracta- 
tion was given, both before sentence and after, which should 
be noted, as well for the wretched palliation which it may 
afford, as for the additional proof it gives that opinions, and 
opinions only, brought him to the stake. In this medley of 
charges the Scriptures are a dream, while Adam, Eve, devils, 
and salvation are truths, and the Saviour a deceiver. We 
have examined no work of Bruno except the De Monade, 
etc., mentioned in the text. A strong though strange theism 
runs through the whole, and Moses, Christ, the Fathers, etc., 
are cited in a manner which excites no remark either way. 
Among the versions of the cause of Bruno's death is atheism : 
but this word was very often used to denote rejection of 
revelation, not merely in the common course of dispute, but 
by such writers, for instance, as Brucker 7 and Morhof . 8 Thus 
Morhof says of the De Monade, etc., that it exhibits no mani- 
fest signs of atheism. What he means by the word is clear 
enough, when he thus speaks of a work which acknowledges 
God in hundreds of places, and rejects opinions as blas- 
phemous in several. The work of Bruno in which his astro- 
nomical opinions are contained is De Monade, etc. (Frank- 
fort, 1591, 8vo). He is the most thorough-going Copernican 
possible, and throws out almost every opinion, true or false, 
which has ever been discussed by astronomers, from the 
theory of innumerable inhabited worlds and systems to that 

7 Johann Jakob Brucker, born at Augsburg in 1696, died there in 
1770. He wrote on the history of philosophy (1731-36, and 1742-44). 

8 Daniel Georg Morhof, born at Wismar in 1639, died at Ltibeck 
in 1691. He was rector of the University of Kiel, and professor of 
eloquence, poetry, and history. 



62 A BUDGET OF PARADOXES. 

of the planetary nature of comets. Libri (vol. iv) 9 has re- 
printed the most striking part of his expressions of Coper- 
nican opinion." 

THIS LEADS TO THE CHURCH QUESTION. 

The Satanic doctrine that a church may employ force 
in aid of its dogma is supposed to be obsolete in England, 
except as an individual paradox ; but this is difficult to settle. 
Opinions are much divided as to what the Roman Church 
would do in England, if she could: any one who doubts 
that she claims the right does not deserve an answer. When 
the hopes of the Tractarian section of the High Church were 
in bloom, before the most conspicuous intellects among them 
had transgressed theif ministry, that they might go to their 
own place, I had the curiosity to see how far it could be 
ascertained whether they held the only doctrine which makes 
me the personal enemy of a sect. I found in one of their 
tracts the assumption of a right to persecute, modified by an 
asserted conviction that force was not efficient. I cannot 
now say that this tract was one of the celebrated ninety ; and 
on looking at the collection I find it so poorly furnished 
with contents, etc., that nothing but searching through three 
thick volumes would decide. In these volumes I find, aug- 
menting as we go on, declarations about the character and 
power of "the Church" which have a suspicious appearance. 
The suspicion is increased by that curious piece of sophis- 
try, No. 87, on religious reserve. The queer paradoxes of 
that tract leave us in doubt as to everything but this, that the 
church (man) is not bound to give his whole counsel in all 
things, and not bound to say what the things are in which 
he does not give it. It is likely enough that some of the 
"rights and liberties" are but scantily described. There is 
now no fear ; but the time was when, if not fear, there might 
be a looking for of fear to come ; nobody could then be so 

'In the Histoire des Sciences Mathematiques, vol. IV, note X, 
pp. 416-435 of the 1841 edition. 



THE CHURCH QUESTION. 63 

sure as we now are that the lion was only asleep. There was 
every appearance of a harder fight at hand than was really 
found needful. 

Among other exquisite quirks of interpretation in the 
No. 87 above mentioned is the following. God himself em- 
ploys reserve; he is said to be decked with light as with a 
garment (the old or prayer-book version of Psalm civ. 2). 
To an ordinary apprehension this would be a strong image 
of display, manifestation, revelation ; but there is something 
more. "Does not a garment veil in some measure that which 
it clothes? Is not that very light concealment?" 

This No. 87, admitted into a series, fixes upon the man- 
agers of the series, who permitted its introduction, a strong 
presumption of that underhand intent with which they were 
charged. At the same time it is honorable to our liberty 
that this series could be published: though its promoters 
were greatly shocked when the Essayists and Bishop Co- 
lenso 1 took a swing on the other side. When No. 90 was 
under discussion, Dr. Maitland, 2 the librarian at Lambeth, 
asked Archbishop Howley 3 a question about No. 89. "I did 
not so much as know there was a No. 89," was the 
answer. I am almost sure I have seen this in print, and quite 
sure that Dr. Maitland told it to me. It is creditable that 
there was so much freedom; but No. 90 was too bad, and 
was stopped. 

The Tractarian mania has now (October 1866) settled 
down into a chronic vestment disease, complicated with fits 
of transubstantiation, which has taken the name of Ritual- 

1 Colenso (1814-1883), missionary bishop of Natal, was one of 
the leaders of his day in the field of higher biblical criticism. De 
Morgan must have admired his mathematical works, which were not 
without merit 

2 Samuel Roffey Maitland, born at London in 1792 ; died at Glou- 
cester in 1866. He was an excellent linguist and a critical student 
of the Bible. He became librarian at Lambeth in 1838. 

'Archbishop Howley (1766-1848) was a thorough Tory. He was 
one of the opponents of the Roman Catholic Relief bill, the Reform 
bill, and the Jewish Civil Disabilities Relief bill. 



64 A BUDGET OF PARADOXES. 

ism. The common sense of our national character will not 
put up with a continuance of this grotesque folly ; millinery 
in all its branches will at last be advertised only over the 
proper shops. I am told that the Ritualists give short and 
practical sermons ; if so, they may do good in the end. The 
English Establishment has always contained those who want 
an excitement ; the New Testament, in its plain meaning, can 
do little for them. Since the Revolution, Jacobitism, Wes- 
leyanism, Evangelicism, Puseyism, 4 and Ritualism, have come 
on in turn, and have furnished hot water for those who 
could not wash without it. If the Ritualists should succeed 
in substituting short and practical teaching for the high- 
spiced lectures of the doctrinalists, they will be remembered 
with praise. John the Baptist would perhaps not have 
brought all Jerusalem out into the wilderness by his plain 
and good sermons: it was the camel's hair and the locusts 
which got him a congregation, and which, perhaps, added 
force to his precepts. When at school I heard a dialogue, 
between an usher and the man who cleaned the shoes, about 

Mr. , a minister, a very corporate body with due area of 

waistcoat. "He is a man of great erudition," said the first. 
"Ah, yes sir," said Joe; "any one can see that who looks 
at that silk waistcoat."] 

OF THOMAS GEPHYRANDER SALICETUS. 

[When I said at the outset that I had only taken books 
from my own store, I should have added that I did not make 
any search for information given as part of a work. Had I 
looked through all my books, I might have made some curi- 
ous additions. For instance, in Schott's Magia Naturalis 1 

* We have, in America at least, almost forgotten the great stir 
made by Edward B. Pusey (1800-1882) in the great Oxford move- 
ment in the middle of the nineteenth century. He was professor of 
Hebrew at Oxford, and canon of Christ Church. 

*That is, his Magia universalis naturae et artis sive recondita 
naturalium et artificialium rerum scientia, Wiirzburg, 1657, 4to, with 
editions at Bamberg in 1671, and at Frankfort in 1677. Gaspard 
Schott (Konigshofen 1608, Wurzburg 1666) was a physicist and 



OF THOMAS GEPHYRANDER SALICETUS. 65 

(vol. iii. pp. 756-778) is an account of the quadrature of 
Gephyrawder, as he is misprinted in Montucla. He was 
Thomas Gephyrander Salicetus ; and he published two edi- 
tions, in 1608 and 1609. 2 I never even heard of a copy of 
either. His work is of the extreme of absurdity : he makes a 
distinction between geometrical and arithmetical fractions, 
and evolves theorems from it. More curious than his quad- 
rature is his name ; what are we to make of it ? If a German, 
he is probably a German form of Bridgeman, and Salicetus 
refers him to Weiden. But Thomas was hardly a German 
Christian name of his time; of 526 German philosophers, 
physicians, lawyers, and theologians who were biographed 
by Melchior Adam, 3 only two are of this name. Of these 
one is Thomas Erastus, 4 the physician whose theological 
writings against the Church as a separate power have given 
the name of Erastians to those who follow his doctrine, 
whether they have heard of him or not. Erastus is little 
known ; accordingly, some have supposed that he must be 
Erastus, the friend of St. Paul and Timothy (Acts xix. 22; 
2 Tim. iv. 20; Rom. xvi. 23), but what this gentleman did 
to earn the character is not hinted at. Few words would 
have done: Gaius (Rom. xvi. 23) has an immortality which 
many more noted men have missed, given by John Bunyan, 
out of seven words of St. Paul. I was once told that the 
Erastians got their name from Blastus, and I could not 
solve bl er: at last I remembered that Blastus was a 
chamberlain 5 as well as Erastus ; hence the association which 

mathematician, devoting most of his attention to the curiosities of 
his sciences. His type of mind must have appealed to De Morgan. 
* Salic etti Quadratura circuit nova, perspicua, expedita, veraque 
turn naturalis, turn geometrica, etc., 1608. Consideratio nova in opus- 
culum Archimedis de circuli dimensione, etc., 1609. 

3 Melchior Adam, who died at Heidelberg in 1622, wrote a col- 
lection of biographies which was published at Heidelberg and Frank- 
fort from 1615 to 1620. 

4 Born at Baden in 1524; died at Basel in 1583. The Erastians 
were related to the Zwinglians, and opposed all power of excom- 
munication and the infliction of penalties by a church. 

5 See Acts xii. 20. 



66 A BUDGET OF PARADOXES. 

caused the mistake. The real heresiarch was a physician 
who died in 1583; his heresy was promulgated in a work, 
published immediately after his death by his widow, De Ex- 
communicatione Ecclesiastic a. He denied the power of ex- 
communication on the principle above stated ; and was an- 
swered by Besa. 8 The work was translated by Dr. R. Lee 7 
(Edinb. 1844, 8vo). The other is Thomas Grynseus, 8 a theo- 
logian, nephew of Simon, who first printed Euclid in Greek ; 
of him Adam says that of works he published none, of 
learned sons four. If Gephyrander were a Frenchman, his 
name is not so easily guessed at ; but he must have been of 
La Saussaye. The account given by Schott is taken from a 
certain Father Philip Colbinus, who wrote against him. 

In some manuscripts lately given to the Royal Society, 
David Gregory, 9 who seems to have seen Gephyrander's 
work, calls him Salicetus Westphalus, which is probably on 
the title-page. But the only Weiden I can find is in Bavaria. 
Murhard has both editions in his Catalogue, but had plainly 
never seen the books: he gives the author as Thomas Gep. 
Hyandrus, Salicettus Westphalus. Murhard is a very old 
referee of mine ; but who the non nominandus was to see 
Montucla's Gephyrauder in Murhard's Gep. Hyandrus, both 
writers being usually accurate?] 

NAPIER ON REVELATIONS. 

A plain discoverie of the whole Revelation of St. John. . . .where- 
tmto are annexed certain oracles of Sibylla. .. .Set Foorth by 
John Napeir L. of Marchiston. London, 1611, 4to. 1 

'Theodore de Bese, a French theologian; born at Vezelay, in 
Burgundy, in 1519; died at Geneva, in 1605. 

7 Dr. Robert Lee (1804-1868) had some celebrity in De Morgan's 
time through his attempt to introduce music and written prayers into 
the service of the Scotch Presbyterian church. 

8 Born at Veringen, Hohenzollern, in 1512; died at Roteln in 
1564. 

9 Born at Kinnairdie, Bannfshire, in 1661 ; died at London in 
1708. His Astronomiae Physicae et Geometriae Elementa, Oxford, 
1702, was an influential work. 

x The title was carelessly copied by De Morgan, not an unusual 



NAPIER ON REVELATIONS. 



67 



The first edition was Edinburgh, 1593, 2 4to. Napier 8 al- 
ways believed that his great mission was to upset the Pope, 
and that logarithms, and such things, were merely episodes 
and relaxations. It is a pity that so many books have been 
written about this matter, while Napier, as good as any, 
is forgotten and unread. He is one of the first who gave 
us the six thousand years. "There is a sentence of the house 
of Elias reserved in all ages, bearing these words : The world 
shall stand six thousand years, and then it shall be con- 
sumed by fire: two thousand yeares voide or without lawe, 
two thousand yeares under the law, and two thousand yeares 
shall be the daies of the Messias . . . . " 

I give Napier's parting salute : it is a killing dilemma : 
"In summar conclusion, if thou o Rome aledges thy- 
self e reformed, and to beleeue true Christianisme, then be- 
leeue Saint John the Disciple, whome Christ loued, pub- 
likely here in this Reuelation proclaiming thy wracke, but 
if thou remain Ethnick in thy priuate thoghts, beleeuing 4 
the old Oracles of the Sibyls reuerently keeped somtime in 
thy Capitol: then doth here this Sibyll proclame also thy 
wracke. Repent therefore alwayes, in this thy latter breath, 
as thou louest thine Eternall salvation. Amen" 
Strange that Napier should not have seen that this ap- 
peal could not succeed, unless the prophecies of the Apo- 
calypse were no true prophecies at all. 

thing in his case. The original reads : A Plaine Discovery, of the 

whole Revelation of S. lohn: set downe in two treatises set 

foorth by lohn Napier L. of Marchiston whereunto are an- 
nexed, certaine Oracles of Sibylla London 1611. 

3 1 have not seen the first edition, but it seems to have appeared 
in Edinburgh, in 1593, with a second edition there in 1594. The 1611 
edition was the third. 

'It seems rather certain that Napier felt his theological work 
of greater importance than that in logarithms. He was born at 
Merchiston, near (now a part of) Edinburgh, in 1550, and died there 
in 1617, three years after the appearance of his Mirifici logarith- 
morum canonis descriptio. 

'Followed, in the third edition, from which he quotes, by a 

comma. 



68 A BUDGET OF PARADOXES. 



OF GILBERT'S DE MAGNETK 

De Magnete magneticisque corporibus, et de magno magnate 
tellure. By William Gilbert London, 1600, folio. There is 
a second edition; and a third, according to Watt. 1 

Of the great work on the magnet there is no need to 
speak, though it was a paradox in its day. The posthumous 
work of Gilbert, "De Mundo nostro sublunari philosophia 
nova" (Amsterdam, 1651, 4to) 2 is, as the title indicates, 
confined to the physics of the globe and its atmosphere. It 
has never excited attention: I should hope it would be ex- 
amined with our present lights. 

OF GIOVANNI BATISTA PORTA. 

Elementorum Curvilineoriuni Libri tres. By John Baptista 
Porta. Rome, 1610, ^o. 1 

This is a ridiculous attempt, which defies description, 
except that it is all about lunules. Porta was a voluminous 
writer. His printer announces fourteen works printed, and 
four to come, besides thirteen plays printed, and eleven 
waiting. His name is, and will be, current in treatises on 
physics for more reasons than one. 

1 There was an edition published at Stettin in 1633. An English 
translation by P. F. Mottelay appeared at London in 1893. Gilbert 
(1540-1603) was physician to Queen Elizabeth and President of the 
College of Physicians at London. His De Magnete was the first 
noteworthy treatise on physics printed in England. He treated of 
the earth as a spherical magnet and suggested the variation and 
declination of the needle as a means of finding latitude at sea. 

2 The title says "ab authoris fratre collectum," although it was 
edited by J. Gruterus. 

1 Porta was born at Naples in 1550 and died there in 1615. He 
studied the subject of lenses and the theory of sight, did some work 
in hydraulics and agriculture, and was well known as an astrologer. 
His Magiae naturalis libri XX was published at Naples in 1589. The 
above title should read curvilineorum. 



CATALDI ON THE QUADRATURE. 69 



CATALDI ON THE QUADRATURE. 

Trattato della quadratura del cerchio. Di Pietro Antonio Ca- 
taldi. Bologna, 1612, folio. 1 

Rheticus, 2 Vieta, and Cataldi are the three untiring com- 
puters of Germany, France, and Italy; Napier in Scotland, 
and Briggs 3 in England, come just after them. This work 
claims a place as beginning with the quadrature of Pelle- 
grino Borello 4 of Reggio, who will have the circle to be 
exactly 3 diameters and 6 %g4 of a diameter. Cataldi, taking 
Van Ceulen's approximation, works hard at the rinding of 
integers which nearly represent the ratio. He had not then 
the continued fraction, a mode of representation which he 
gave the next year in his work on the square root. He has 
but twenty of Van Ceulen's thirty places, which he takes 
from Clavius 5 : and any one might be puzzled to know whence 
the Italians got the result ; Van Ceulen, in 1612, not having 
been translated from Dutch. But Clavius names his com- 
rade Gruenberger, and attributes the approximation to them 

1 Cataldi was born in 1548 and died at Bologna in 1626. He was 
professor of mathematics at Perugia, Florence, and Bologna, and is 
known in mathematics chiefly for his work in continued fractions. 
He was one of the scholarly men of his day. 

2 Georg Joachim Rheticus was born at Feldkirch in 1514 and died 
at Caschau, Hungary, in 1576. He was one of the most prominent 
pupils of Copernicus, his Narratio de libris revolutionism Copernici 
(Dantzig, 1540) having done much to make the theory of his master 
known. 

8 Henry Briggs, who did so much to make logarithms known, and 
who used the base 10, was born at Warley Wood, in Yorkshire, in 
1560, and died at Oxford in 1630. He was Savilian professor of 
mathematics at Oxford, and his grave may still be seen there. 

4 He lived at "Reggio nella Emilia" in the i6th and I7th centuries. 
His Regola e modo facilissimo di quadrare il cerchio was published 
at Reggio in 1609. 

8 Christoph Klau (Clavius) was born at Bamberg in 1537, and 
died at Rome in 1612. He was a Jesuit priest and taught mathe- 
matics in the Jesuit College at Rome. He wrote a number of works 
on mathematics, including excellent text-books on arithmetic and 
algebra. 



70 A BUDGET OF PARADOXES. 

jointly; "Lud. aCollen et Chr. Gruenbergerus* invenerunt," 
which he had no right to do, unless, to his private knowl- 
edge, Gruenberger had verified Van Ceulen. And Gruen- 
berger only handed over twenty of the places. But here is 
one instance, out of many, of the polyglot character of the 
Jesuit body, and its advantages in literature. 

OF LANSBERGIUS. 

Philippi Lausbergii Cyclometriae Novae Libri Duo. Middleburg, 
1616, 4U). 1 

This is one of the legitimate quadratures, on which I 
shall here only remark that by candlelight it is quadrature 
under difficulties, for all the diagrams are in red ink. 

A TEXT LEADING TO REMARKS ON PRESTER JOHN. 

Recherches Curieuses des Mesures du Monde. By S. C. de V. 
Paris, 1626, 8vo (pp. 48). * 

It is written by some Count for his son; and if all the 
French nobility would have given their sons the same kind 
of instruction about rank, the old French aristocracy would 
have been as prosperous at this moment as the English 
peerage and squireage. I sent the tract to Capt. Speke, 2 
shortly after his arrival in England, thinking he might like 

"Christopher Gruenberger, or Grienberger, was born at Halle 
in Tyrol in 1561, and died at Rome in 1636. He was, like Clavius, 
a Jesuit and a mathematician, and he wrote a little upon the sub- 
ject of projections. His Prospcctiva nova coelestis appeared at 
Rome in 1612. 

1 The name should, of course, be Lansbergii in the genitive, and 
is so in the original title. Philippus Lansbergius was born at Ghent 
in 1560, and died at Middelburg in 1632. He was a Protestant 
theologian, and was also a physician and astronomer. He was a 
well-known supporter of Galileo and Copernicus. His Commen- 
tationes in motum terrae diurnum et annuum appeared at Middel- 
burg in 1630 and did much to help the new theory. 

1 1 have never seen the work. It is rare. 

"The African explorer, born in Somersetshire in 1827, died at 
Bath in 1864. He was the first European to cross Central Africa 
from north to south. He investigated the sources of the Nile. 



A TEXT LEADING TO REMARKS ON PRESTER JOHN. 71 

to see the old names of the Ethiopian provinces. But I 
first made a copy of all that relates to Prester John, 3 himself 
a paradox. The tract contains, inter alia, an account of the 
four empires ; of the great Turk, the great Tartar, the great 
Sophy, and the great Prester John. This word great 
(grand'), which was long used in the phrase "the great 
Turk," is a generic adjunct to an emperor. Of the Tartars 
it is said that "c'est vne nation prophane et barbaresque, 
sale et vilaine, qui mangent la chair demie crue, qui boiuent 
du laict de jument, et qui n'vsent de nappes et seruiettes 
que pour essuyer leurs bouches et leurs mains." 4 Many 
persons have heard of Prester John, and have a very indis- 
tinct idea of him. I give all that is said about him, since 
the recent discussions about the Nile may give an interest 
to the old notions of geography. 5 

"Le grand Prestre Jean qui est le quatriesme en rang, 
est Empereur d'Ethiopie, et des Abyssins, et se vante 
d'estre issu de la race de Dauid, comme estant descendu de 
la Royne de Saba, Royne d'Ethiopie, laquelle estant venue 
en Hierusalem pour voir la sagesse de Salomon, enuiron 
Tan du monde 2952, s'en retourna grosse d'vn fils qu'ils 
nomment Moylech, duquel ils disent estre descendus en ligne 
directe. Et ainsi il se glorifie d'estre le plus ancien Mo- 
narque de la terre, disant que son Empire a dure plus de 
trois mil ans, ce que nul autre Empire ne peut dire. Aussi 
met-il en ses tiltres ce qui s'ensuit: Nous, N. Souuerain en 
mes Royaumes, vniquement ayme de Dieu, colomne de la 
foy, sorty de la race de luda, etc. Les limites de cet Empire 
touchent a la mer Rouge, et aux montagnes d'Azuma vers 

'Prester (Presbyter, priest) John, the legendary Christian king 
whose realm, in the Middle Ages, was placed both in Asia and in 
Africa, is first mentioned in the chronicles of Otto of Freisingen in 
the I2th century. In the I4th century his kingdom was supposed to 
be Abyssinia. 

*"It is a profane and barbarous nation, dirty and slovenly, who 
eat their meat half raw and drink mare's milk, and who use table- 
cloths and napkins only to wipe their hands and mouths." 

8 For translation see page 73. 



72 A BUDGET OF PARADOXES. 

I'Orient, et du coste de 1'Occident, il est borne du fleuue du 
Nil, qui le separe de la Nubie, vers le Septentrion il a 
I'^igypte, et au Midy les Royaumes de Congo, et de Mo- 
zambique, sa longueur contenant quarante degre, qui font 
mille vingt cinq lieues, et ce depuis Congo ou Mozambique 
qui sont au Midy, iusqu'en yEgypte qui est au Septentrion, et 
sa largeur contenant depuis le Nil qui est a 1'Occident, ius- 
qu'aux montagnes d'Azuma, qui sont a I'Orient, sept cens 
vingt cinq lieues, qui font vingt neuf degrez. Cet empire 
a sous soy trente grandes Prouinces, sgavoir, Medra, Gaga, 
Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, 
Fungy, Angote, Cigremaon, Gorga Cafatez, Zastanla, Zeth, 
Early, Belangana, Tygra, Gorgany, Barganaza, d'Ancut, 
Dargaly Ambiacatina, Caracogly, Amara. Maon (sic), 
Guegiera, Bally, Dobora et Macheda. Toutes ces Pro- 
uinces cy dessus sont situees iustement sous la ligne equi- 
noxiale, entres les Tropiques de Capricorne, et de Cancer. 
Mais elles s'approchent de nostre Tropique, de deux cens 
cinquante lieues plus qu'elles ne font de 1'autre Tropique. 
Ce mot de Prestre Jean signifie grand Seigneur, et n'est pas 
Prestre comme plusieurs pense, il a este tousiours Chrestien, 
mais souuent Schismatique : maintenant il est Catholique, et 
reconnaist le Pape pour Souuerain Pontife. Fay veu quel- 
quVn des ses Euesques, estant en Hierusalem, auec lequel 
i'ay confere souuent par le moyen de nostre trucheman: 
il estoit d'vn port graue et serieux, succiur (sic) en son 
parler, mais subtil a merueilles en tout ce qu'il disoit. II 
prenoit grand plaisir au recit que je luy faisais de nos belles 
ceremonies, et de la grauite de nos Prelats en leurs habits 
Pontificaux, et autres choses que je laisse pour dire, que 
1'Ethiopien est ioyoux et gaillard, ne ressemblant en rien 
a la salete du Tartare, ny a Taffreux regard du miserable 
Arabe, mais ils sont fins et cauteleux, et ne se fient en per- 
sonne, soupgonneux a merueilles, et fort devotieux, ils ne 
sont du tout noirs comme Ton croit, i'entens parler de ceux 
qui ne sont pas sous la ligne Equinoxiale, ny trop proches 



A TEXT LEADING TO REMARKS ON PRESTER JOHN. 73 

d'icelle, car ceux qui sont dessous sont les Mores que nous 
voyons." 6 

It will be observed that the author speaks of his con- 
versation with an Ethiopian bishop, about that bishop's sov- 
ereign. Something must have passed between the two 
which satisfied the writer that the bishop acknowledged his 
own sovereign under some title answering to Prester John. 

' "The great Prester John, who is the fourth in rank, is emperor 
of Ethiopia and of the Abyssinians, and boasts of his descent from 
the race of David, as having descended from the Queen of Sheba, 
Queen of Ethiopia. She, having gone to Jerusalem to see the wisdom 
of Solomon, about the year of the world 2952, returned pregnant 
with a son whom they called Moylech, from whom they claim descent 
in a direct line. And so he glories in being the most ancient monarch 
in the world, saying that his empire has endured for more than 
three thousand years, which no other empire is able to assert. He 
also puts into his titles the following: 'We, the sovereign in my 
realms, uniquely beloved of God, pillar of the faith, sprung from the 
race of Judah, etc.' The boundaries of this empire touch the Red 
Sea and the mountains of Azuma on the east, and on the western 
side it is bordered by the River Nile which separates it from Nubia. 
To the north lies Egypt, and to the south the kingdoms of Congo 
and Mozambique. It extends forty degrees in length, or one thou- 
sand twenty-five leagues, from Congo or Mozambique on the south 
to Egypt on the north ; and in width it reaches from the Nile on the 
west to the mountains of Azuma on the east, seven hundred twenty- 
five leagues, or twenty-nine degrees. This empire contains thirty 
large provinces, namely Medra, Gaga, Alchy, Cedalon, Mantro, Fina- 
zam, Barnaquez, Ambiam, Fungy, Angote, Cigremaon, Gorga, Cafa- 
tez, Zastanla, Zeth, Early, Belangana, Tygra, Gorgany, Barganaza, 
d'Ancut, Dargaly, Ambiacatina, Caracogly, Amara. Maon (sic), 
Guegiera, Bally, Dobora, and Macheda. All of these provinces are situ- 
ated directly under the equinoctial line between the tropics of Capri- 
corn and Cancer; but they are two hundred fifty leagues nearer our 
tropic than the other. The name of Prester John signifies Great 
Lord, and is not Priest [Presbyter] as many think. He has always 
been a Christian, but often schismatic. At the present time he is a 
Catholic and recognizes the Pope as sovereign pontiff. I met one of 
his bishops in Jerusalem, and often conversed with him through the 
medium of our guide. He was of grave and serious bearing, pleas- 
ant of speech, but wonderfully subtle in everything he said. He took 
great delight in what I had to relate concerning our beautiful cere- 
monies and the dignity of our prelates in their pontifical vestments. 
As to other matters I will only say that the Ethiopian is joyous and 
merry, not at all like the Tartar in the matter of filth, nor like the 
wretched Arab. They are refined and subtle, trusting no one, wonder- 
fully suspicious, and very devout. They are not at all black as is 
commonly supposed, by which I refer to those who do not live under 
the equator or too near to it, for these are Moors as we shall see.' 

With respect to this translation it should be said that the original 



74 A BUDGET OF PARADOXES. 



CONCERNING A TRACT BY FIENUS. 

De Cometa anni 1618 dissertationes Thomse Fieni 1 et Liberti 

Fromondi 2 Equidem Thomae Fieni epistolica qusestio, An 

verum sit Ccelum moveri et Terram quiescere? London, 1670, 
8vo. 

This tract of Fienus against the motion o the earth is 
a reprint of one published in 1619. 8 I have given an account 
of it as a good summary of arguments of the time, in the 
Companion to the Almanac for 1836. 

forms of the proper names have been preserved, although they are 
not those found in modern works. It should also be stated that 
the meaning of Prester is not the one that was generally accepted 
by scholars at the time the work was written, nor is it the one 
accepted to-day. There seems to be no doubt that the word is de- 
rived from Presbyter as stated in note 3 on page 71, since the above- 
mentioned chronicles of Otto, bishop of Freisingen about the middle 
of the twelfth century, states this fact clearly. Otto received his in- 
formation from the bishop of Gabala (the Syrian Jibal) who told 
him the story of John, rex et sacevdos, or Presbyter John as he liked 
to be called. He goes on to say: "Should it be asked why, with all 
this power and splendor, he calls himself merely 'presbyter/ this is 
because of his humility, and because it was not fitting for one whose 
server was a primate and king, whose butler an archbishop and 
king, whose chamberlain a bishop and king, whose master of the 
horse an archimandrite and king, whose chief cook an abbot and 
king, to be called by such titles as these." 

1 Thomas Fienus (Fyens) was born at Antwerp in 1567 and died 
in 1631. He was professor of medicine at Louvain. Besides the 
editions mentioned below, his De cometis anni 1618 appeared at 
Leipsic in 1656. He also wrote a Disputatio an coelum moveatur 
et terra quiescat, which appeared at Antwerp in 1619, and again at 
Leipsic in 1656. 

a Libertus Fromondus (1587-^.1653), a Belgian theologian, dean 
of the College Church at Harcourt, and professor at Louvain. The 
name also appears as Froidmont and Froimont. 

9 L. Fromondi. . . .meteorologicorum libri sex. Cut accessit T. 
Fieni et L. Fromondi dissertationes de cometa anni 1618. . . .This is 
from the 1670 edition. The 1619 edition was published at Antwerp. 
The Meteorologicorum libri VI, appeared at Antwerp in 1627. He 
also wrote Anti-Aristarchus sive orbis terrae immobilis liber unicus 
(Antwerp, 1631) ; Labyrrinthus sive de compositione continui liber 
unus, Philosophis, Mathematicis, Theologis utilis et jucundus (Ant- 
werp, 1631) and Vesta sive Anti-Aristarchi vindex adversus Jac. 
Lansbergium (Philippi filium) et copernicanos (Antwerp, 1634). 



ON BACON'S NOVUM ORGANUM. 75 

ON SNELL'S WORK. 

Willebrordi Snellii. R. F. Cyclometricus. Leyden, 1621, 4to. 

This is a celebrated work on the approximative quad- 
rature, which, having the suspicious word cyclometricus, 
must be noticed here for distinction. 1 

ON BACON'S NOVUM ORGANUM. 

1620. In this year, Francis Bacon 1 published his Novum 
Organum, 2 which was long held in England but not until 
the last century to be the work which taught Newton and 
all his successors how to philosophize. That Newton never 
mentions Bacon, nor alludes in any way to his works, passed 
for nothing. Here and there a paradoxer ventured not to find 
all this teaching in Bacon, but he was pronounced blind. In 
our day it begins to be seen that, great as Bacon was, and 
great as his book really is, he is not the philosophical father 
of modern discovery. 

But old prepossession will find reason for anything. A 
learned friend of mine wrote to me that he had discovered 
proof that Newton owned Bacon for his master: the proof 
was that Newton, in some of his earlier writings, used the 

1 Snell was born at Leyden in 1591, and died there in 1626. He 
studied under Tycho Brahe and Kepler, and is known for Snell's 
law of the refraction of light He was the first to determine the 
size of the earth by measuring the arc of a meridian with any fair 
degree of accuracy. The title should read : Willebrordi Snellii R. F. 
Cyclometricus, de circuit dimensione secundum Logistarum abacos, 
et ad Mechanicem accuratissima. .. . 

1 Bacon was born at York House, London, in 1561, and died near 
Highgate, London, in 1626. His Novum Organum Scientiarum or New 
Method of employing the reasoning faculties in the pursuits of Truth 
appeared at London in 1620. He had previously published a work 
entitled Of the Proficience and Advancement of Learning, divine and 
humane ^(London, 1605), which again appeared in 1621. His De 
augmentis scientiarum Libri IX appeared at Paris in 1624, and his 
Historia naturalis et experimental de ventis at Leyden in 1638. He 
was successively solicitor general, attorney general, lord chancellor 
(1619), Baron Verulam and Viscount St. Albans. He was deprived 
of office and was imprisoned in the Tower of London in 1621, but 
was later pardoned. 

8 The Greek form, Organon, is sometimes used. 



76 A BUDGET OF PARADOXES. 

phrase experimentum crucis, which is Bacon's. Newton 
may have read some of Bacon, though no proof of it ap- 
pears. I have a dim idea that I once saw the two words 
attributed to the alchemists : if so, there is another explana- 
tion; for Newton was deeply read in the alchemists. 

I subjoin a review which I wrote of the splendid edition 
of Bacon by Spedding, 3 Ellis, 4 and Heath. 5 All the opinions 
therein expressed had been formed by me long before : most 
of the materials were collected for another purpose. 



The Works of Francis Bacon. Edited by James Spedding, R. 
Leslie Ellis, and Douglas D. Heath. 5 vols. 1 

No knowledge of nature without experiment and ob- 
servation: so said Aristotle, so said Bacon, so acted Coper- 
nicus, Tycho Brahe, 2 Gilbert, Kepler, Galileo, Harvey, etc., 
before Bacon wrote. 3 No derived knowledge until experi- 
ment and observation are concluded: so said Bacon, and 
no one else. We do not mean to say that he laid down his 
principle in these words, or that he carried it to the utmost 
extreme: we mean that Bacon's ruling idea was the collec- 

8 James Spedding (1808-1881), fellow of Cambridge, who devoted 
his life to his edition of Bacon. 

4 R. Leslie Ellis (1817-1859), editor of the Cambridge Mathemat- 
ical Journal. He also wrote on Roman aqueducts, on Boole's Laws 
of Thought, and on the formation of a Chinese dictionary. 

6 Douglas Derion Heath (1811-1897), a classical and mathematical 
scholar. 

1 There have been numerous editions of Bacon's complete works, 
including the following: Frankfort, 1665; London, 1730, 1740, 1764, 
1765, 1778, 1893, 1807, 1818, 1819, 1824, 1825-36, 1857-74, 1877. The 
edition to which De Morgan refers is that of 1857-74, 14 vols., of 
which five were apparently out at the time he wrote. There were 
also French editions in 1800 and 1835. 

2 So in the original for Tycho Brahe. 

8 In general these men acted before Bacon wrote, or at any rate 
before he wrote the Novum Organum, but the statement must not 
be taken too literally. The dates are as follows: Copernicus, 1473- 
1543; Tycho Brahe, 1546-1601; Gilbert, 1540-1603; Kepler, 1571-1630; 
Galileo, 1564-1642; Harvey, 1578-1657. For example, Harvey's Exer- 
citatio Anatomica de Motu Cordis et Sanguinis did not appear until 
1628, and his Exercitationes de Generatione until 1651. 



ON BACON'S NOVUM ORGANUM. 77 

tion of enormous masses of facts, and then digested pro- 
cesses of arrangement and elimination, so artistically con- 
trived, that a man of common intelligence, without any un- 
usual sagacity, should be able to announce the truth sought 
for. Let Bacon speak for himself, in his editor's English: 

"But the course I propose for the discovery of sciences 
is such as leaves but little to the acuteness and strength of 
wits, but places all wits and understandings nearly on a 
level. For, as in the drawing of a straight line or a per- 
fect circle, much depends on the steadiness and practice of 
the hand, if it be done by aim of hand only, but if with the 
aid of rule or compass little or nothing, so it is exactly 
with my plan. . . .For my way of discovering sciences goes 
far to level men's wits, and leaves but little to individual 
excellence ; because it performs everything by the surest 
rules and demonstrations." 

To show that we do not strain Bacon's meaning, we add 
what is said by Hooke, 4 whom we have already mentioned 
as his professed disciple, and, we believe, his only disciple 
of the day of Newton. We must, however, remind the 
reader that Hooke was very little of a mathematician, and 
spoke of algebra from his own idea of what others had 
told him: 

"The intellect is not to be suffered to act without its 
helps, but is continually to be assisted by some method or 
engine, which shall be as a guide to regulate its actions, 
so as that it shall not be able to act amiss. Of this engine, 
no man except the incomparable Verulam hath had any 
thoughts, and he indeed hath promoted it to a very good 
pitch ; but there is yet somewhat more to be added, which 
he seemed to want time to complete. By this, as by that 

4 Robert Hooke (1635-1703) studied under Robert Boyle at Ox- 
ford. He was "Curator of Experiments" to the Royal Society and 
its secretary, and was professor of geometry at Gresham College, 
London. It is true that he was "very little of a mathematician" 
although he wrote on the motion of the earth ( 1674) , on helioscopes 
and other instruments (1675), on the rotation of Jupiter (1666), 
and on barometers and sails. 



78 A BUDGET OF PARADOXES. 

art of algebra in geometry, 'twill be very easy to proceed 
in any natural inquiry, regularly and certainly .... For as 
'tis very hard for the most acute wit to find out any difficult 
problem in geometry without the help of algebra .... and 
altogether as easy for the meanest capacity acting by that 
method to complete and perfect it, so will it be in the in- 
quiry after natural knowledge." 

Bacon did not live to mature the whole of this plan. Are 
we really to believe that if he had completed the Instauratio 
we who write this and who feel ourselves growing bigger 
as we write it should have been on a level with Newton 
in physical discovery? Bacon asks this belief of us, and 
does not get it. But it may be said, Your business is with 
what he did leave, and with its consequences. Be it so. 
Mr. Ellis says: "That his method is impracticable cannot, 
I think, be denied, if we reflect not only that it never has 
produced any result, but also that the process by which 
scientific truths have been established cannot be so presented 
as even to appear to be in accordance with it." That this 
is very true is well known to all who have studied the 
history of discovery : those who deny it are bound to estab- 
lish either that some great discovery has been made by 
Bacon's method we mean by the part peculiar to Bacon 
or, better still, to show that some new discovery can be 
made, by actually making it. No general talk about induc- 
tion: no reliance upon the mere fact that certain experi- 
ments or observations have been made ; let us see where 
Bacon's induction has been actually used or can be used. 
Mere induction, enumeratio simplex, is spoken of by him- 
self with contempt, as utterly incompetent. For Bacon 
knew well that a thousand instances may be contradicted 
by the thousand and first: so that no enumeration of in- 
stances, however large, is "sure demonstration," so long as 
any are left. 

The immortal Harvey, who was inventing we use the 
word in its old sense the circulation of the blood, while 



ON BACON'S NOVUM ORGANUM. 79 

Bacon was in the full flow of thought upon his system, may 
be trusted to say whether, when the system appeared, he 
found any likeness in it to his own processes, or what would 
have been any help to him, if he had waited for the Novum 
Organum. He said of Bacon, "He writes philosophy like 
a Lord Chancellor." This has been generally supposed to 
be only a sneer at the sutor ultra crepidam ; but we cannot 
help suspecting that there was more intended by it. To us, 
Bacon is eminently the philosopher of error prevented, not 
of progress facilitated. When we throw off the idea of 
being led right, and betake ourselves to that of being kept 
from going wrong, we read his writings with a sense of 
their usefulness, his genius, and their probable effect upon 
purely experimental science, which we can be conscious of 
upon no other supposition. It amuses us to have to add 
that the part of Aristotle's logic of which he saw the value 
was the book on refutation of fallacies. Now is this not 
the notion of things to which the bias of a practised lawyer 
might lead him? In the case which is before the Court, 
generally speaking, truth lurks somewhere about the facts, 
and the elimination of all error will show it in the residuum. 
The two senses of the word law come in so as to look almost 
like a play upon words. The judge can apply the law so soon 
as the facts are settled: the physical philosopher has to de- 
duce the law from the facts. Wait, says the judge, until 
the facts are determined: did the prisoner take the goods 
with felonious intent? did the defendant give what amounts 
to a warranty? or the like. Wait, says Bacon, until all the 
facts, or all the obtainable facts, are brought in: apply my 
rules of separation to the facts, and the result shall come 
out as easily as by ruler and compasses. We think it pos- 
sible that Harvey might allude to the legal character of 
Bacon's notions : we can hardly conceive so acute a man, 
after seeing what manner of writer Bacon was, meaning 
only that he was a lawyer and had better stick to his busi- 
ness. We do ourselves believe that Bacon's philosophy 



80 A BUDGET OF PARADOXES. 

more resembles the action of mind of a common-law judge 
not a Chancellor than that of the physical inquirers who 
have been supposed to follow in his steps. It seems to us 
that Bacon's argument is, there can be nothing of law but 
what must be either perceptible, or mechanically deducible, 
when all the results of law, as exhibited in phenomena, 
are before us. Now the truth is, that the physical philos- 
opher has frequently to conceive law which never was in 
his previous thought to educe the unknown, not to choose 
among the known. Physical discovery would be very easy 
work if the inquirer could lay down his this, his that, and 
his t'other, and say, "Now, one of these it must be; let us 
proceed to try which." Often has he done this, and failed ; 
often has the truth turned out to be neither this, that, nor 
t'other. Bacon seems to us to think that the philosopher 
is a judge who has to choose, upon ascertained facts, which 
of known statutes is to rule the decision : he appears to us 
more like a person who is to write the statute-book, with 
no guide except the cases and decisions presented in all their 
confusion and all their conflict. 

Let us take the well-known first aphorism of the Novum 
Organum : 

"Man being the servant and interpreter of nature, can do 
and understand so much, and so much only, as he has ob- 
served in fact or in thought of the course of nature : beyond 
this he neither knows anything nor can do anything." 

This aphorism is placed by Sir John Herschel 5 at the 
head of his Discourse on the Study of Natural Philosophy : 
a book containing notions of discovery far beyond any of 
which Bacon ever dreamed ; and this because it was written 

8 The son of the Sir William mentioned below. He was born in 
1792 and died in 1871. He wrote a treatise on light (1831) and one 
on astronomy (1836), and established an observatory at the Cape 
of Good Hope where he made observations during 1834-1838, pub- 
lishing them in 1847. On his return to England he was knighted, 
and in 1848 was made president of the Royal Society. The title of 
the work to which reference is made is : A preliminary discourse on 
the Study of Natural Philosophy. It appeared at London in 1831. 



ON BACON'S NOVUM ORGANUM. 81 

after discovery, instead of before. Sir John Herschel, in 
his version, has avoided the translation of re vel mente ob- 
servaverit, and gives us only "by his observation of the 
order of nature." In making this the opening of an ex- 
cellent sermon, he has imitated the theologians, who often 
employ the whole time of the discourse in stuffing matter 
into the text, instead of drawing matter out of it. 'By ob- 
servation he (Herschel) means the whole course of dis- 
covery, observation, hypothesis, deduction, comparison, etc. 
The type of the Baconian philosopher as it stood in his 
mind, had been derived from a noble example, his own 
father, William Herschel, 6 an inquirer whose processes would 
have been held by Bacon to have been vague, insufficient, 
compounded of chance work and sagacity, and too meagre 
of facts to deserve the name of induction. In another work, 
his treatise on Astronomy, 7 Sir John Herschel, after noting 
that a popular account can only place the reader on the 
threshold, proceeds to speak as follows of all the higher 
departments of science. The italics are his own: 

"Admission to its sanctuary, and to the privileges and 
feelings of a votary, is only to be gained by one means 
sound and sufficient knowledge of mathematics, the great 
instrument of all exact inquiry, without which no man can 
ever make such advances in this or any other of the higher 
departments of science as can entitle him to form an inde- 
pendent opinion on any subject of discussion within their 
range" 

How is this? Man can know no more than he gets 
from observation, and yet mathematics is the great instru- 
ment of all exact inquiry. Are the results of mathematical 
deduction results of observation? We think it likely that 

"Sir William was born at Hanover in 1738 and died at Slough, 
near Windsor, in 1822. He discovered the planet Uranus and six 
satellites, besides two satellites of Saturn. He was knighted by 
George III. 

7 This was the work of 1836. He also published a work entitled 
Outlines of Astronomy in 1849. 



82 A BUDGET OF PARADOXES. 

Sir John Herschel would reply that Bacon, in coupling 
together observare re and observare mente, has done what 
some wags said Newton afterwards did in his study-door 
cut a large hole of exit for the large cat, and a little hole 
for the little cat. 8 But Bacon did no such thing: he never 
included any deduction under observation. To mathematics 
he had a dislike. He averred that logic and mathematics 
should be the handmaids, not the mistresses, of philosophy. 
He meant that they should play a subordinate and subsequent 
part in the dressing of the vast mass of facts by which dis- 
covery was to be rendered equally accessible to Newton and 
to us. (Bacon himself was very ignorant of all that had been 
done by mathematics ; and, strange to say, he especially ob- 
jected to astronomy being handed over to the mathemati- 
cians. Leverrier and Adams, calculating an unknown planet 
into visible existence by enormous heaps of algebra, furnish 
the last comment of note on this specimen of the goodness 
of Bacon's views. The following account of his knowledge 
of what had been done in his own day or before it, is Mr. 
Spedding's collection of casual remarks in Mr. Ellis's several 
prefaces : 

"Though he paid great attention to astronomy, dis- 
cussed carefully the methods in which it ought to be studied, 
constructed for the satisfaction of his own mind an elaborate 
theory of the heavens, and listened eagerly for the news 
from the stars brought by Galileo's telescope, he appears to 
have been utterly ignorant of the discoveries which had 
just been made by Kepler's calculations. Though he com- 
plained in 1623 of the want of compendious methods for 
facilitating arithmetical computations, especially with regard 
to the doctrine of Series, and fully recognized the importance 
of them as an aid to physical inquiries he does not say a 
word about Napier's Logarithms, which had been published 
only nine, years before and reprinted more than once in the 

"While Newton does not tell the story, he refers in the Prindpia 
(1714 edition, p. 293) to the accident caused by his cat. 



83 



interval. He complained that no considerable advance had 
been made in geometry beyond Euclid, without taking any 
notice of what had been done by Archimedes and Apollonius. 
He saw the importance of determining accurately the spe- 
cific gravity of different substances, and himself attempted 
to form a table of them by a rude process of his own, with- 
out knowing of the more scientific though still imperfect 
methods previously employed by Archimedes, Ghetaldus, 9 and 
Porta. He speaks of the evprjKa of Archimedes in a manner 
which implies that he did not clearly apprehend either the 
nature of the problem to be solved or the principles upon 
which the solution depended. In reviewing the progress 
of mechanics, he makes no mention of Archimedes himself, 
or of Stevinus, 10 Galileo, Guldinus, 11 or Ghetaldus. He makes 
no allusion to the theory of equilibrium. He observes that 
a ball of one pound weight will fall nearly as fast through 
the air as a ball of two, without alluding to the theory of 
the acceleration of falling bodies, which had been made 
known by Galileo more than thirty years before. He pro- 
poses an inquiry with regard to the lever namely, whether 
in a balance with arms of different length but equal weight 
the distance from the fulcrum has any effect upon the in- 
clination, though the theory of the lever was as well under- 
stood in his own time as it is now. In making an experiment 

"Marino Ghetaldi (1566-1627), whose Promotus 'Archimedes ap- 
peared at Rome in 1603, Nonnullae propositiones de parabola at 
Rome in 1603, and Apollonius redivivus at Venice in 1607. He was 
a nobleman and was ambassador from Venice to Rome. 

10 Simon Steyin (born at Bruges, 1548; died at the Hague, 1620). 
He was an engineer and a soldier, and his La Disme (1585) was 
the first separate treatise on the decimal fraction. The contribution 
referred to above is probably that on the center of gravity of three 
bodies (1586). 

"Habakuk Guldin (1577-1643), who took the name Paul on his 
conversion to Catholicism. He became a Jesuit, and was professor 
of mathematics at Vienna and later at Gratz. In his Centrobaryca 
sen de centra gravitatis trium specierum quantitatis continuae (1635), 
of the edition of 1641, appears the Pappus rule for the volume of a 
solid formed by the revolution of a plane figure about an axis, often 
spoken of as Guldin' s Theorem. 



84 A BUDGET OF PARADOXES. 

of his own to ascertain the cause of the motion of a wind- 
mill, he overlooks an obvious circumstance which makes the 
experiment inconclusive, and an equally obvious variation 
of the same experiment which would have shown him that 
his theory was false. He speaks of the poles of the earth 
as fixed, in a manner which seems to imply that he was not 
acquainted with the precession of the equinoxes ; and in 
another place, of the north pole being above and the south 
pole below, as a reason why in our hemisphere the north 
winds predominate over the south." 

Much of this was known before, but such a summary 
of Bacon's want of knowledge of the science of his own 
time was never yet collected in one place. We may add, 
that Bacon seems to have been as ignorant of Wright's 12 
memorable addition to the resources of navigation as of 
Napier's addition to the means of calculation. Mathematics 
was beginning to be the great instrument of exact inquiry: 
Bacon threw the science aside, from ignorance, just at the 
time when his enormous sagacity, applied to knowledge, 
would have made him see the part it was to play. If New- 
ton had taken Bacon for his master, not he, but somebody 
else, would have been Newton. 13 

ON METEOROLOGICAL OBSERVATORIES. 

There is an attempt at induction going on, which has 
yielded little or no fruit, the observations made in the 
meteorological observatories. This attempt is carried on 
in a manner which would have caused Bacon to dance for 
joy; for he lived in times when Chancellors did dance. 

"Edward Wright was born at Graveston, Norfolkshire, in 1560, 
and died at London in 1615. He was a fellow of Caius College, 
Cambridge, and in his work entitled The correction of certain errors 
in Navigation (1599) he gives the principle of Mercator's projec- 
tion. He translated the Portuum investigandorum ratio of Stevin in 
1599- 

18 De Morgan never wrote a more suggestive sentence. Its mes- 
sage is not for his generation alone. 



BASIS OF MODERN DISCOVERY. 85 

Russia, says M. Biot, 1 is covered by an army of meteoro- 
graphs, with generals, high officers, subalterns, and privates 
with fixed and defined duties of observation. Other coun- 
tries have also their systematic observations. And what 
has come of it? Nothing, says M. Biot, and nothing will 
ever come of it ; the veteran mathematician and experimental 
philosopher declares, as does Mr. Ellis, that no single branch 
of science has ever been fruitfully explored in this way. 
There is no special object, he says. Any one would suppose 
that M. Biot's opinion, given to the French Government 
upon the proposal to construct meteorological observatories 
in Algeria (Comptes Rendus, vol. xli, Dec. 31, 1855), was 
written to support the mythical Bacon, modern physics, 
against the real Bacon of the Novum Organum. There is 
no special object. In these words lies the difference between 
the two methods. 

[In the report to the Greenwich Board of Visitors for 
1867 Mr. Airy, 2 speaking of the increase of meteorological 
observatories, remarks, "Whether the effect of this move- 
ment will be that millions of useless observations will be 
added to the millions that already exist, or whether some- 
thing may be expected to result which will lead to a meteoro- 
logical theory, I cannot hazard a conjecture." This is a 
conjecture, and a very obvious one: if Mr. Airy would have 
given 2%d. for the chance of a meteorological theory formed 
by masses of observations, he would never have said what 
I have quoted.] 

BASIS OF MODERN DISCOVERY. 

Modern discoveries have not been made by large collec- 
tions of facts, with subsequent discussion, separation, and re- 

1 The eminent French physicist, Jean Baptiste Biot (1779-1862), 
professor in the College de France. His work Sur les observatoires 
meteor ologiques appeared in 1855. 

8 George Biddell Airy (1801-1892), professor of astronomy and 
physics at Cambridge, and afterwards director of the Observatory 
at Greenwich. 



86 A BUDGET OF PARADOXES. 

suiting deduction of a truth thus rendered perceptible. A 
few facts have suggested an hypothesis, which means a 
supposition, proper to explain them. The necessary results 
of this supposition are worked out, and then, and not till 
then, other facts are examined to see if these ulterior results 
are found in nature. The trial of the hypothesis is the 
special object: prior to which, hypothesis must have been 
started, not by rule, but by that sagacity of which no de- 
scription can be given, precisely because the very owners 
of it do not act under laws perceptible to themselves. 1 The 
inventor of hypothesis, if pressed to explain his method, 
must answer as did Zerah Colburn, 2 when asked for his mode 
of instantaneous calculation. When the poor boy had been 
bothered for some time in this manner, he cried out in a 
huff, "God put it into my head, and I can't put it into yours." 3 

1 De Morgan would have rejoiced in the role played by Intuition 
in the mathematics of to-day, notably among the followers of Pro- 
fessor Klein. 

2 Colburn was the best known of the calculating boys produced 
in America. He was born at Cabot, Vermont, in 1804, and died at 
Norwich, Vermont, in 1840. Having shown remarkable skill in 
numbers as early as 1810, he was taken to London in 1812, whence 
he toured through Great Britain and to Paris. The Earl of Bristol 
placed him in Westminster School (1816-1819). On his return to 
America he became a preacher, and later a teacher of languages. 

8 The history of calculating boys is interesting. Mathieu le Coc 
(about 1664), a boy of Lorraine, could extract cube roots at sight 
at the age of eight. Tom Fuller, a Virginian slave of the eighteenth 
century, although illiterate, gave the number of seconds in 7 years 
17 days 12 hours after only a minute and a half of thought Jede- 
diah Buxton, an Englishman of the eighteenth century, was studied 
by the Royal Society because of his remarkable powers. Ampere, 
the physicist, made long calculations with pebbles at the age of four. 
Gauss, one of the few infant prodigies to become an adult prodigy, 
corrected his father's payroll at the age of three. One of the most 
remarkable of the French calculating boys was Henri Mpndeux. 
He was investigated by Arago, Sturm, Cauchy, and Liouville, for 
the Academic des Sciences, and a report was written by Cauchy. 
His specialty was the solution of algebraic problems mentally. He 
seems to have calculated squares and cubes by a binomial formula 
of his own invention. He died in obscurity, but was the subject 
of a Biographie by Jacoby (1846). George P. Bidder, the Scotch 
engineer (1806-1878), was exhibited as an arithmetical prodigy at 
the age of ten, and did not attend school until he was twelve. Of 
the recent cases two deserve special mention, Inaudi and Diamandi. 



BASIS OF MODERN DISCOVERY. 87 

Wrong hypotheses, rightly worked from, have produced 
more useful results than unguided observation. But this is 
not the Baconian plan. Charles the Second, when informed 
of the state of navigation, founded a Baconian observatory 
at Greenwich, to observe, observe, observe away at the 
moon, until her motions were known sufficiently well to 
render her useful in guiding the seaman. And no doubt 
Flamsteed's 4 observations, twenty or thirty of them at least, 
were of signal use. But how ? A somewhat fanciful thinker, 
one Kepler, had hit upon the approximate orbits of the 
planets by trying one hypothesis after another: he found 
the ellipse, which the Platonists, well despised of Bacon, 
and who would have despised him as heartily if they had 
known him, had investigated and put ready to hand nearly 
2000 years before. 5 The sun in the focus, the motions of 
the planet more and more rapid as they approach the sun, 
led Kepler and Bacon would have reproved him for his 
rashness to imagine that a force residing in the sun might 
move the planets, a force inversely as the distance. Bouil- 
laud, 6 upon a fanciful analogy, rejected the inverse distance, 

Jacques Inaudi (born in 1867) was investigated for the Academic 
in 1892 by a commission including Poincare, Charcot, and Binet. 
(See the Revue des Deux Mondes, June 15, 1892, and the laboratory 
bulletins of the Sorbonne). He has frequently exhibited his re- 
markable powers in America. Pericles Diamandi was investigated 
by the same commission in 1893. See Alfred Binet, Psychologic des 
Grands Calculateurs et Joueurs d'Echecs, Paris, 1894. 

4 John Flamsteed's (1646-1719) "old white house" was the first 
Greenwich observatory. He was the Astronomer Royal and first 
head of this observatory. 

5 It seems a pity that De Morgan should not have lived to lash 
those of our time who are demanding only the immediately prac- 
tical in mathematics. His satire would have been worth the read- 
ing against those who seek to stifle the science they pretend to foster. 

'Ismael Bouillaud, or Boulliau, was born in 1605 and died at 
Paris in 1694. He was well known as an astronomer, mathemati- 
cian, and jurist. He lived with De Thou at Paris, and accompanied 
him to Holland. He traveled extensively, and was versed in the 
astronomical work of the Persians and Arabs. It was in his 
Astronomia philolaica, opus novum (Paris, 1645) that he attacked 
Kepler's laws. His tables were shown to be erroneous by the fact 
that the solar eclipse did not take place as predicted by him in 1645. 



88 A BUDGET OF PARADOXES. 

and, rejecting the force altogether, declared that if such a 
thing there were, it would be as the inverse square of the 
distance. Newton, ready prepared with the mathematics 
of the subject, tried the fall of the moon towards the earth, 
away from her tangent, and found that, as compared with 
the fall of a stone, the law of the inverse square did hold 
for the moon. He deduced the ellipse, he proceeded to 
deduce the effect of the disturbance of the sun upon the 
moon, upon the assumed theory of universal gravitation. 
He found result after result of his theory in conformity with 
observed fact: and, by aid of Flamsteed's observations, 
which amended what mathematicians call his constants, he 
constructed his lunar theory. Had it not been for Newton, 
the whole dynasty of Greenwich astronomers, from Flam- 
steed of happy memory, to Airy whom Heaven preserve, 7 
might have worked away at nightly observation and daily 
reduction, without any remarkable result: looking forward, 
as to a millennium, to the time when any man of moderate 
intelligence was to see the whole explanation. What are 
large collections of facts for? To make theories from, says 
Bacon: to try ready-made theories by, says the history of 
discovery: it's all the same, says the idolater: nonsense, 
say we! 

Time and space run short: how odd it is that of the 
three leading ideas of mechanics, time, space, and matter, 
the first two should always fail a reviewer before the third. 
We might dwell upon many points, especially if we at- 
tempted a more descriptive account of the valuable edition 
before us. No one need imagine that the editors, by their 
uncompromising attack upon the notion of Bacon's influence 
common even among mathematicians and experimental phi- 
losophers, have lowered the glory of the great man whom 
it was, many will think, their business to defend through 
thick and thin. They have given a clearer notion of his 

T As it did, until 1892, when Airy had reached the ripe age of 
ninety-one. 



THE REAL VALUE OF BACON^S WORKS. 89 

excellencies, and a better idea of the power of his mind, 
than ever we saw given before. Such a correction as theirs 
must have come, and soon, for as Hallam says after noting 
that the Novum Organum was never published separately 
in England, Bacon has probably been more read in the 
last thirty years now forty than in the two hundred years 
which preceded. He will now be more read than ever he 
was. The history of the intellectual world is the history 
of the worship of one idol after another. No sooner is it 
clear that a Hercules has appeared among men, than all 
that imagination can conceive of strength is attributed to 
him, and his labors are recorded in the heavens. The time 
arrives when, as in the case of Aristotle, a new deity is 
found, and the old one is consigned to shame and reproach. 
A reaction may afterwards take place, and this is now hap- 
pening in the case of the Greek philosopher. The end of the 
process is, that the opposing deities take their places, side 
by side, in a Pantheon dedicated not to gods, but to heroes. 

THE REAL VALUE OF BACON'S WORKS. 

Passing over the success of Bacon's own endeavors to 
improve the details of physical science, which was next to 
nothing, and of his method as a whole, which has never 
been practised, we might say much of the good influence 
of his writings. Sound wisdom, set in sparkling wit, must 
instruct and amuse to the end of time: and, as against 
error, we repeat that Bacon is soundly wise, so far as he 
goes. There is hardly a form of human error within his 
scope which he did not detect, expose, and attach to a satir- 
ical metaphor which never ceases to sting. He is largely 
indebted to a very extensive reading; but the thoughts of 
others fall into his text with such a close-fitting compact- 
ness that he can make even the words of the Sacred Writers 
pass for his own. A saying of the prophet Daniel, rather 
a hackneyed quotation in our day, Multi pertransibunt, et 
augebitur scientia, stands in the title-page of the first edition 



90 A BUDGET OF PARADOXES. 

of Montucla's History of Mathematics as a quotation from 
Bacon and it is not the only place in which this mistake 
occurs. When the truth of the matter, as to Bacon's sys- 
tem, is fully recognized, we have little fear that there will 
be a reaction against the man. First, because Bacon will 
always live to speak for himself, for he will not cease to be 
read: secondly, because those who seek the truth will find 
it in the best edition of his works, and will be most ably led 
to know what Bacon was, in the very books which first 
showed at large what he was not. 

THE CONGREGATION OF THE INDEX, ON COPERNICUS. 

In this year ( 1620) appeared the corrections under which 
the Congregation of the Index i. e., the Committee of 
Cardinals which superintended the Index of forbidden books 
proposed to allow the work of Copernicus to be read. I 
insert these conditions in full, because they are often alluded 
to, and I know of no source of reference accessible to a 
twentieth part of those who take interest in the question. 

By a decree of the Congregation of the Index, dated 
March 5, 1616, the work of Copernicus, and another of 
Didacus Astunica, 1 are suspended donee corrigantur, as teach- 
ing: 

"Falsam illam doctrinam Pythagoricam, divinae que 
Scripturae omnino adversantem, de mobilitate Terrae et im- 
mobilitate Solis." 2 

But a work of the Carmelite Foscarini 3 is: 

1 Didaci a Stunica. .. .In 7ob commentaria appeared at Toledo in 
1584. 

'"The false Pythagorean doctrine, absolutely opposed to the Holy 
Scriptures, concerning the mobility of the earth and the immobility 
of the sun/' 

8 Paolo Antonio Foscarini (1580-1616), who taught theology and 
philosophy at Naples and Messina, was one of the first to champion 
the theories of Copernicus. This was in his Lettera sopra f opinion* 
de' Pittagorici e del Copernico, della mobilita della Terra e stabilita 
del Sole, e il nuovo pittagorico sistema del mondo, 4to,^ Naples, 1615. 
The condemnation of the Congregation was published in the follow- 
ing spring, and in the year of Foscarini's death at the early age of 
thirty-six. 



THE CONGREGATION OF THE INDEX, ON COPERNICUS. 91 

"Omnino prohibendum atque damnandum," because "os- 
tendere conatur prsef atam doctrinam .... consonam esse veri- 
tati et non adversari Sacrae Scripturse."* 

Works which teach the false doctrine of the earth's mo- 
tion are to be corrected; those which declare the doctrine 
conformable to Scripture are to be utterly prohibited. 

In a "Monitum ad Nicolai Copernici lectorem, ejusque 
emendatio, permissio, et correctio," dated 1620 without the 
month or day, permission is given to reprint the work of 
Copernicus with certain alterations ; and, by implication, to 
read existing copies after correction in writing. In the pre- 
amble the author is called nobilis astrologus-, not a compli- 
ment to his birth, which was humble, but to his fame. The 
suspension was because: 

"Sacrse Scripturae, ejusque verse et Catholicse interpre- 
tation! repugnantia (quod in homine Christiano minime 
tolerandum) non per hypothesin tractare, sed ut verissima 
adstruere non dubitat!" 5 

And the corrections relate: 

"Locis in quibus non ex hypothesi, sed asserendo de situ 
et motu Terrae disputat." 6 

That is, the earth's motion may be an hypothesis for 
elucidation of the heavenly motions, but must not be as- 
serted as a fact. 

(In Pref. circa finem.) "Copernicus. Si fortasse erunt 
/AaratoAoyot, qui cum omnium Mathematum ignari sint, tamen 
de illis judicium sibi summunt, propter aliquem locum scrip- 
turse, male ad suum propositum detortum, ausi fuerint meum 

"To be wholly prohibited and condemned," because "it seeks to 
show that the aforesaid doctrine is consonant with truth and is not 
opposed to the Holy Scriptures." 

" "As repugnant to the Holy Scriptures and to its true and Catho- 
lic interpretation (which in a Christian man cannot be tolerated in 
the least), he does not hesitate to treat (of his subject) 'by hypoth- 
esis' but he even adds 'as most true' I" 

'"To the places in which he discusses not by hypothesis but by 
making assertions concerning the position and motion of the earth." 



92 A BUDGET OF PARADOXES. 

hoc institutum reprehendere ac insectari: illos nihil moror 
adeo tit etiam illorum judicium tanquam temerarium con- 
temnam. Non enim obscurum est Lactantium, celebrem 
alioqui scriptorem, sed Mathematicum parum, admodum 
pueriliter de forma terrse loqui, cum deridet eos, qui terram 
globi formam habere prodiderunt. Itaque non debet mirum 
videri studiosis, si qui tales nos etiam videbunt. Mathemata 
Mathematicis scribuntur, quibus et hi nostri labores, si me 
non fallit opinio, videbuntur etiam Reipub. ecclesiastics 
conducere aUquid .... Emend. Ibi si fortasse dele omnia, 
usque ad verbum hi nostri labores et sic accommoda Ccete- 
rum hi nostri labores." 7 

All the allusion to Lactantius, who laughed at the notion 
of the earth being round, which was afterwards found true, 
is to be struck out. 

(Cap. 5. lib. i. p. 3) "Copernicus. Si tamen attentius 
rem consideremus, videbitur hsec qusestio nondum absoluta, 
et idcirco minime contemnenda. Emend. Si tamen atten- 
tius rem consideremus, nihil refert an Terram in medio 
Mundi, an extra Medium existere, quoad solvendas cceles- 
tium motuum apparentias existimemus." 8 

7 "Copernicus, If by chance there shall be vain talkers who, al- 
though ignorant of all mathematics, yet taking it upon themselves 
to sit in judgment upon the subject on account of a certain passage 
of Scripture badly distorted for their purposes, shall have dared 
to criticize and censure this teaching of mine, I pay no attention 
to them, even to the extent of despising their judgment as rash. 
For it is not unknown that Lactantius, a writer of prominence 
in other lines although but little versed in mathematics, spoke 
very childishly about the form of the earth when he ridiculed 
those who declared that it was spherical. Hence it should not seem 
strange to the learned if some shall look upon us in the same way. 
Mathematics is written for mathematicians, to whom these labors 
of ours will seem, if I mistake not, to add something even to the 

republic of the Church Emend. Here strike out everything from 

'if by chance' to th'e words 'these labors of ours/ and adapt it thus : 
'But these labors of ours/" 

8 "Copernicus. However if we consider the matter more carefully 
it will be seen that the investigation is not yet completed, and there- 
fore ought by no means to be condemned. Emend. However, if we 
consider the matter more carefully it is of no consequence whether 



THE CONGREGATION OF THE INDEX, ON COPERNICUS. 93 

We must not say the question is not yet settled, but 
only that it may be settled either way, so far as mere ex- 
planation of the celestial motions is concerned. 

(Cap. 8. lib. i.) "Totum hoc caput potest expungi, quia 
ex professo tractat de veritate motus Terrse, dum solvit 
veterum rationes probantes ejus quietem. Cum tamen prob- 
lematice videatur loqui ; ut studiosis satisfiat, seriesque et 
ordo libri integer maneat ; emendetur ut infra." 9 

A chapter which seems to assert the motion should per- 
haps be expunged; but it may perhaps be problematical; 
and, not to break up the book, must be amended as below. 

(p. 6.) "Copernicus. Cur ergo hesitamus adhuc, mobili- 
tatem illi formae suse a natura congruentem concedere, ma- 
gisquam quod totus labatur mundus, cujus finis ignoratur, 
scirique nequit, neque fateamur ipsius cotidianae revolutio- 
nis in coelo apparentiam esse, et in terra veritatem? Et 
hsec perinde se habere, ac si diceret Virgilianus yEneas: 
Provehimur portu .... Emend. Cur ergo non possum mobi- 
litatem illi formse suse concedere, magisque quod totus laba- 
tur mundus, cujus finis ignoratur scirique nequit, et quse 
apparent in ccelo, perinde se habere ac si. . . ." 10 

we regard the earth as existing in the center of the universe or 
outside of the center, so far as the solution of the phenomena of 
celestial movements is concerned." 

"The whole of this chapter may be cut out, since it avowedly 
treats of the truth of the earth's motion, while it refutes the reasons 
of the ancients proving its immobility. Nevertheless, since it seems 
to speak problematically, in order that it may satisfy the learned and 
keep intact the sequence and unity of the book let it be emended 
as below." 

"Copernicus. Therefore why do we still hesitate to concede to 
it motion which is by nature consistent with its form, the more so 
because the whole universe is moving, whose end is not and cannot 
be known, and not confess that there is in the sky an appearance of 
daily revolution, while on the earth there is the truth of it ? And in 
like manner these things are as if Virgil's ^Eneas should say, 'We 
are borne from the harbor'.... Emend. Hence I cannot concede 
motion to this form, the more so because the universe would fall, 
whose end is not and cannot be known, and what appears in the 
heavens is just as if. ..." 



94 A BUDGET OF PARADOXES. 

"Why should we hesitate to allow the earth's motion," 
must be altered into "I cannot concede the earth's motion." 

(p. 7.) "Copernicus. Addo etiam, quod satis absurdum 
videretur, continenti sive locanti motum adscribi, et non 
potius contento et locato, quod est terra. Emend. Addo etiam 
difficilius non esse contento et locato, quod est Terra, motum 
adscribere, quam continenti." 11 

We must not say it is absurd to refuse motion to the 
contained and located, and to give it to the containing and 
locating; say that neither is more difficult than the other. 

(p. 7.) "Copernicus. Vides ergo quod ex his omnibus 
probabilior sit mobilitas Terrae, quam ejus quies, prsesertim 
in cotidiana revolutione, tanquam terrse maxime propria. 
Emend. Fides. . . .delendus est usque ad finem capitis." 12 

Strike out the whole of the chapter from this to the 
end; it says that the motion of the earth is the most prob- 
able hypothesis. 

(Cap. 9. lib. i. p. 7.) "Copernicus. Cum igitur nihil pro- 
hibeat mobilitatem Terrae, videndum nunc arbitror, an etiam 
plures illi motus conveniant, ut possit una errantium syde- 
rum existimari. Emend. Cum igitur Terram moveri as- 
sumpserim, videndum nunc arbitror, an etiam illi plures 
possint convenire motus." 13 

^"Copernicus. I also add that it would seem very absurd that 
motion should be ascribed to that which contains and ^locates, and 
not rather to that which is contained and located, that is the earth. 
Emend. I also add that it is not more difficult to ascribe motion to 
the contained and located, which is the earth, than to that which 
contains it." 

" "Copernicus. You see, therefore, that from all these things 
the motion of the earth is more probable than its immobility, espe- 
cially in the daily revolution which is as it were a particular prop- 
erty of it. Emend. Omit from 'You see' to the end of the chapter." 

13 "Copernicus. Therefore, since there is nothing to hinder the 
motion of the earth, it seems to me that we should consider whether 
it has several motions, to the end that it may be looked upon as one 
of the moving stars. Emend. Therefore, since I have assumed that 
the earth moves, it seems to me that we should consider whether it 
has several motions." 



THE CONGREGATION OF THE INDEX, ON COPERNICUS. 95 

We must not say that nothing prohibits the motion of 
the earth, only that having assumed it, we may inquire 
whether our explanations require several motions. 

(Cap. 10. lib. i. p. 9.) "Copernicus. Non pudet nos 
f ateri .... hoc potius in mobilitate terrse verificari. Emend. 
Non pudet nos assumere .... hoc consequenter in mobilitate 
verificari." 14 

(Cap. 10. lib. i. p. 10.) "Copernicus. Tanta nimirum est 
divina haec. Opt. Max. fabrica. Emend. Dele ilia verba 
postrema." 15 

(Cap. ii. lib. i. 16 ) "Copernicus. De triplici motu telluris 
demonstratio. Emend. De hypothesi triplicis motus Terrse, 
ejusque demonstratione." 17 

(Cap. 10. lib. iv. p. 122. 18 ) "Copernicus. De magnitudine 
horum trium siderum, Solis, Lunse, et Terrse. Emend. Dele 
verba horum trium siderum, quia terra non est sidus, ut 
facit earn Copernicus." 19 

We must not say we are not ashamed to acknowledge; as- 
sume is the word. We must not call this assumption a 
Divine work. A chapter must not be headed demonstration, 
but hypothesis. The earth must not be called a star; the 
word implies motion. 

It will be seen that it does not take much to reduce 
Copernicus to pure hypothesis. No personal injury being 
done to the author who indeed had been 17 years out of 

4 "Copernicus. We are not ashamed to acknowledge that 

this is preferably verified in the motion of the earth. Emend. We 

are not ashamed to assume that this is consequently verified in 

the motion." 

5 "Copernicus. So divine is surely this work of the Best and 
Greatest. Emend. Strike out these last words." 

18 This should be Cap. u, lib. i, p. 10. 

7 "Copernicus. Demonstration of the threefold motion of the 
earth. Emend. On the hypothesis of the threefold motion of the 
earth and its demonstration." 

18 This should be Cap. 20, lib. iv, p. 122. 

8 "Copernicus. Concerning the size of these three stars, the sun, 
the moon, and the earth. Emend. Strike out the words 'these three 
stars,' because the earth is not a star as Copernicus would make it." 



96 A BUDGET OF PARADOXES. 

reach the treatment of his book is now an excellent joke. 
It is obvious that the Cardinals of the Index were a little 
ashamed of their position, and made a mere excuse of a 
few corrections. Their mode of dealing with chap. 8, this 
problematice videtur loqui, ut studiosis satisfiat is an ex- 
cuse to avoid corrections. But they struck out the stinging 
allusion to Lactantius 21 in the preface, little thinking, honest 
men, for they really believed what they said that the light 
of Lactantius would grow dark before the brightness of 
their own. 

THE CONVOCATION AT OXFORD EQUALLY AT FAULT. 

1622. I make no reference to the case of Galileo, except 
this. I have pointed out (Penny Cycl. Suppl. "Galileo"; 
Engl Cycl. "Motion of the Earth") that it is clear the ab- 
surdity was the act of the Italian Inquisition for the private 
and personal pleasure of the Pope, who knew that the course 
he took would not commit him as Pope and not of the 
body which calls itself the Church. Let the dirty proceed- 
ing have its right name. The Jesuit Riccioli, 1 the stoutest 
and most learned Anti-Copernican in Europe, and the Puri- 
tan Wilkins, a strong Copernican and Pope-hater, are equally 
positive that the Roman Church never pronounced any de- 
cision : and this in the time immediately following the ridic- 
ulous proceeding of the Inquisition. In like manner a deci- 
sion of the Convocation of Oxford is not a law of the Eng- 
lish Church; which is fortunate, for that Convocation, in 
1622, came to a decision quite as absurd, and a great deal 

20 He seems to speak problematically in order to satisfy the 
learned. 

21 One of the Church Fathers, born about 250 A. D., and died about 
330, probably at Treves. He wrote Divinarum Institutionum Libri 
VII, and other controversial and didactic works against the learning 
and philosophy of the Greeks. 

1 Giovanni Battista Riccioli (1598-1671) taught philosophy and 
theology at Parma and Bologna, and was later professor of astron- 
omy. His Almagestum novum appeared in 1651, and his Argomento 
fisico-matematico contro il moto diurno della terra in 1668. 



THE CONVOCATION AT OXFORD EQUALLY AT FAULT. 97 

more wicked than the declaration against the motion of the 
earth. The second was a foolish mistake; the first was a 
disgusting surrender of right feeling. The story is told 
without disapprobation by Anthony Wood, who never exag- 
gerated anything against the university of which he is wri- 
ting eulogistic history. 

In 1622, one William Knight 2 put forward in a sermon 
preached before the University certain theses which, looking 
at the state of the times, may have been improper and pos- 
sibly of seditious intent. One of them was that the bishop 
might excommunicate the civil magistrate: this proposition 
the clerical body could not approve, and designated it by the 
term erronea* the mildest going. But Knight also declared 
as follows: 

"Subditis mere privatis, si Tyrannus tanquam latro aut 
stuprator in ipsos faciat impetum, et ipsi nee potestatem ordi- 
nariam implorare, nee alia ratione effugere periculum pos- 
sint, in presenti periculo se et suos contra tyrannum, sicut 
contra privatum grassatorem, defendere licet." 4 

That is, a man may defend his purse or a woman her 
honor, against the personal attack of a king, as against that 
of a private person, if no other means of safety can be found. 
The Convocation sent Knight to prison, declared the propo- 
sition "falsa, periculosa, et impia" and enacted that all ap- 
plicants for degrees should subscribe this censure, and make 
oath that they would neither hold, teach, nor defend Knight's 
opinions. 

The thesis, in the form given, was unnecessary and im- 
proper. Though strong opinions of the king's rights were 
advanced at the time, yet no one ventured to say that, min- 

2 He was a native of Arlington, Sussex, and a pensioner of Christ's 
College, Cambridge. In 1603 he became a master of arts at Oxford. 

8 Straying, i. e., from the right way. 

4 "Private subjects may, in the presence of danger, defend them- 
selves or their families against a monarch as against any malefactor, 
if the monarch assaults them like a bandit or a ravisher, and pro- 
vided they are unable to summon the usual protection and cannot in 
any way escape the danger." 



98 A BUDGET OF PARADOXES. 

isters and advisers apart, the king might personally break 
the law ; and we know that the first and only attempt which 
his successor made brought on the crisis which cost him 
his throne and his head. But the declaration that the propo- 
sition was false far exceeds in all that is disreputable the 
decision of the Inquisition against the earth's motion. We 
do not mention this little matter in England. Knight was 
a Puritan, and Neal 5 gives a short account of his sermon. 
From comparison with Wood, 6 I judge that the theses, as 
given, were not Knight's words, but the digest which it was 
customary to make in criminal proceedings against opinion. 
This heightens the joke, for it appears that the qualifiers 
of the Convocation took pains to present their condemnation 
of Knight in the terms which would most unequivocally 
make their censure condemn themselves. This proceeding 
took place in the interval between the two proceedings 
against Galileo: it is left undetermined whether we must 
say pot-kettle-pot or kettle-pot-kettle. 

Liberti Fromondi. . . .Ant-Aristarchus, sive orbis terrae immo- 
bilis. Antwerp, 1631, 8vo. T 

This book contains the evidence of an ardent opponent 
of Galileo to the fact, that Roman Catholics of the day did 
not consider the decree of the Index or of the Inquisition 
as a declaration of their Church. Fromond would have been 
glad to say as much, and tries to come near it, but con- 
fesses he must abstain. See Penny Cyclop. Suppl. "Galileo," 
and Eng. Cycl "Motion of the Earth." The author of a 
celebrated article in the Dublin Review, in defence of the 

"Daniel Neal (1678-1743), an independent minister, wrote a His- 
tory of the Puritans that appeared in 1732. The account may be 
found in the New York edition of 1843-44, vol. I, p. 271. 

6 Anthony Wood (1632-1695), whose Historia et Antiquitates 
Universitatis Oxoniensis (1674) and Athenae Oxoniensis (1691) are 
among the classics on Oxford. 

7 Part of the title, not here quoted, shows the nature of the work 
more clearly: "liber unicus, in quo decretum S. Congregations S. 
R. E. Cardinal, an. 1616, adversus Pythagorico-Copernicanos editum, 
defenditur." 



THE METIUS APPROXIMATION. 99 

Church of Rome, seeing that Drinkwater Bethune 8 makes 
use of the authority of Fromondus, but for another purpose, 
sneers at him for bringing up a "musty old Professor." 
If he had known Fromondus, and used him he would have 
helped his own case, which is very meagre for want of 
knowledge. 9 

Advis a Monseigneur reminentissime Cardinal Due de Richelieu, 
sur la Proposition faicte par le Sieur Morin pour 1'invention 
des longitudes. Paris, 1634, 8vo. 10 

This is the Official Report of the Commissioners ap- 
pointed by the Cardinal, of whom Pascal is the one now 
best known, to consider Morin's plan. See the full account 
in Delambre, Hist. Astr. Mod. ii. 236, etc. 

THE METIUS APPROXIMATION. 

Arithmetica et Geometria practica. By Adrian Metius. Leyden, 
1640, 4to. 1 

This book contains the celebrated approximation guessed 
at by his father, Peter Metius, 2 namely that the diameter is 

8 This was John Elliot Drinkwater Bethune (1801-1851), the 
statesman who did so much for legislative and educational reform 
in India. His father, John Drinkwater Bethune, wrote a history of 
the siege of Gibraltar. 

9 The article referred to is about thirty years old; since it ap- 
peared another has been given (Dubl. Rev., Sept. 1865) which is of 
much greater depth. In it will also be found the Roman view of 
Bishop Virgil (ante, p. 32). A. De M. 

10 Jean Baptiste Morin (1583-1656), in his younger days physician 
to the Bishop of Boulogne and the Duke of Luxemburg, became in 
1630 professor of mathematics at the College Royale. His ^ chief 
contribution to the problem of the determination of longitude is his 
Longitudinum terrestrium et coelestium nova et hactenus optata 
scientia (1634). He also wrote against Copernicus in his Famosi 
problematis de telluris motu vel quiete hactenus optata solutio (1631), 
and against Lansberg in his Responsio pro telluris quiete (1634). 

1 The work appeared at Leyden in 1626, at Amsterdam in 1634, at 
Copenhagen in 1640, and again at Leyden in 1650. The title of the 
1640 edition is Arithmeticae Libri II et Geometriae Libri VI. The 
work on which it is based is the Arithmeticae et Geometriae Prac- 
tica, which appeared in 1611. 

2 The father's name was Adriaan, and Lalande says that it was 
Montucla who first made the mistake of calling him Peter, thinking 



100 A BUDGET OF PARADOXES. 

to the circumference as 113 to 355. The error it at the rate 
'of about a foot in 2,000 miles. Peter Metius, having his 
attention called to the subject by the false quadrature of 
Duchesne, found that the ratio lay between 33 %oe an d 37 %2o- 
He then took the liberty of taking the mean of both numera- 
tors and denominators, giving 35 %is. He had no right to pre- 
sume that this mean was better than either of the extremes ; 
nor does it appear positively that he did so. He published 
nothing; but his son Adrian, 3 when Van Ceulen's work 
showed how near his father's result came to the truth, first 
made it, known in the work above. (See Eng. Cyclop., art. 
"Quadrature.") 

ON INHABITABLE PLANETS. 

A discourse concerning a new world and another planet, in two 

books. London, 1640, Svo. 1 
Cosmotheoros : or conjectures concerning the planetary worlds 

and their inhabitants. Written in Latin, by Christianus Huy- 

ghens. This translation was first published in 1698. Glasgow 

1757, 8vo. [The original is also of 1698.] 2 

The first work is by Bishop Wilkins, being the third 
edition, [first in 1638] of the first book, "That the Moon 
may be a Planet" ; and the first edition of the second work, 

that the initials P. M. stood for Petrus Metius, when in reality they 
stood for piae memoriae ! The ratio ""/us was known in China hun- 
dreds of years before his time. See note 3, page 52. 

'Adrian Metius (1571-1635) was professor of medicine at the 
University of Franeker. His work was, however, in the domain of 
astronomy, and in this domain he published several treatises. 

1 The first edition was entitled : The Discovery of a World in the 
Moone. Or, a Discourse Tending to prove that 'tis probable there 
may be another habitable World in that Planet. 1638, Svo. The 
fourth edition appeared in 1684. John Wilkins (1614-1672) was 
Warden of Wadham College, Oxford ; master of Trinity, Cambridge ; 
and, later, Bishop of Chester. He was influential in founding the 
Royal Society. 

2 The first edition was entitled: C. Hugenii Koo-^o^ewpos, give de 
Terris coelestibus, earumque ornatu, conjecturae, The Hague, 1698, 
4to. There were several editions. It was also translated into French 
(1718), and there was another English edition (1722). Huyghens 
(1629-1695) was one of the best mathematical physicists of his time. 



ON INHABITABLE PLANETS. O 

"That the Earth may be a Planet." [See more under the 
reprint of 1802.] Whether other planets be inhabited or 
not, that is, crowded with organisations some of them having 
consciousness, is not for me to decide; but I should be 
much surprised if, on going to one of them, I should find 
it otherwise. The whole dispute tacitly assumes that, if 
the stars and planets be inhabited, it must be by things of 
which we can form some idea. But for aught we know, 
what number of such bodies there are, so many organisms 
may there be, of which we have no way of thinking nor 
of speaking. This is seldom remembered. In like manner 
it is usually forgotten that the matter of other planets may 
be of different chemistry from ours. There may be no 
oxygen and hydrogen in Jupiter, which may have gens of 
its own. 3 But this must not be said: it would limit the 
omniscience of the a priori school of physical inquirers, the 
larger half of the whole, and would be very unphilosophical. 
Nine-tenths of my best paradoxers come out from among 
this larger half, because they are just a little more than of 
it at their entrance. 

There was a discussion on the subject some years ago, 
which began with 

The plurality of worlds : an Essay. London, 1853, 8vo. [By Dr. 
Wm. Whewell, Master of Trinity College, Cambridge]. A 
dialogue on the plurality of worlds, being a supplement to the 
Essay on that subject. [First found in the second edition, 
1854; removed to the end in subsequent editions, and separate 
copies issued.] 4 

A work of skeptical character, insisting on analogies 
which prohibit the positive conclusion that the planets, stars, 
etc., are what we should call inhabited worlds. It produced 

8 It is hardly necessary to say that science has made enormous 
advance in the chemistry of the universe since these words were 
written. 

4 William Whewell (1794-1866) is best known through his History 
of the Inductive Sciences (1837) and Philosophy of the Inductive 
Sciences (1840). 



102 A BUDGET OF PARADOXES. 

several works and a large amount of controversy in reviews. 
The last predecessor of whom I know was 

Plurality of Worlds By Alexander Maxwell. Second Edition. 

London, 1820, 8vo. 

This work is directed against the plurality by an author 
who does not admit modern astronomy. It was occasioned 
by Dr. Chalmers's 5 celebrated discourses on religion in con- 
nection with astronomy. The notes contain many citations 
on the gravity controversy, from authors now very little 
read: and this is its present value. I find no mention of 
Maxwell, not even in Watt. 6 He communicated with man- 
kind without the medium of a publisher; and, from Vieta 
till now, this method has always been favorable to loss of 
books. 

A correspondent informs me that Alex. Maxwell, who 
wrote on the plurality of worlds, in 1820, was a law-book- 
seller and publisher (probably his own publisher) in Bell 
Yard. He had peculiar notions, which he was fond of dis- 
cussing with his customers. He was a bit of a Sweden- 
borgian. 

INHABITED PLANETS IN FICTION. 
There is a class of hypothetical creations which do not 
belong to my subject, because they are acknowledged to be 
fictions, as those of Lucian, 1 Rabelais, 2 Swift, Francis God- 

5 Thomas Chalmers (1780-1847), the celebrated Scotch preacher. 
These discourses were delivered while he was minister in a large 
parish in the poorest part of Glasgow, and in them he attempted to 
bring science into harmony with the Bible. He was afterwards 
professor of moral philosophy at St. Andrew's (1823-28), and pro- 
fessor of theology at Edinburgh (1828). He became the leader of 
a schism from the Scotch Presbyterian Church, the Free Church. 

"That is, in Robert Watt's (1774-1819) Bibliotheca Britannica 
(posthumous, 1824). Nor is it given in the Dictionary of National 
Biography. 

1 The late Greek satirist and poet, c. I2O-C. 200 A. D. 

* Francois Rabelais (c. 1490-1553) the humorist who created Pan- 
tagruel (1533) and Gargantua (1532). His work as a physician and 
as editor of the works of Galen and Hippocrates is less popularly 
known. 



INHABITED PLANETS IN FICTION. 103 

win, 3 Voltaire, etc. All who have more positive notions as to 
either the composition or organization of other worlds, than 
the reasonable conclusion that our Architect must be quite 
able to construct millions of other buildings on millions of 
other plans, ought to rank with the writers just mentioned, 
in all but self-knowledge. Of every one of their systems 
I say, as the Irish Bishop said of Gulliver's book, I don't 
believe half of it. Huyghens had been preceded by Fon- 
tenelle, 4 who attracted more attention. Huyghens is very 
fanciful and very positive ; but he gives a true account of his 
method. "But since there's no hopes of a Mercury to carry 
us such a journey, we shall e'en be contented with what's 
in our power: we shall suppose ourselves there. ..." And 
yet he says, "We have proved that they live in societies, 
have hands and feet. ..." Kircher 5 had gone to the stars 
before him, but would not find any life in them, either animal 
or vegetable. 

The question of the inhabitants of a particular planet 
is one which has truth on one side or the other : either there 
are some inhabitants, or there are none. Fortunately, it is 
of no consequence which is true. But there are many 
cases where the balance is equally one of truth and false- 
hood, in which the choice is a matter of importance. My 
work selects, for the most part, sins against demonstration: 
but the world is full of questions of fact or opinion, in which 
a struggling minority will become a majority, or else will 

8 Francis Godwin (1562-1633) bishop of Llandaff and Hereford. 
Besides some valuable historical works he wrote The Man in the 
Moone, or a Discourse of a voyage thither by Domingo Consoles, 
the Speed Messenger of London, 1638. 

* Bernard Le Bovier de Fontenelle (1657-1757), historian, critic, 
mathematician, Secretary of the Academic des Sciences, and member 
of the Academic Franchise. His Entretien sur la pluralite des 
mondes appeared at Paris in 1686. 

"Athanasius Kircher (1602-1680), Jesuit, professor of mathe- 
matics and philosophy, and later of Hebrew and Syriac, at Wurz- 
burg; still later professor of mathematics and Hebrew at Rome. 
He wrote several works on physics. His collection of mathematical 
instruments and other antiquities became the basis of the Kircherian 
Museum at Rome. 



104 A BUDGET OF PARADOXES. 

be gradually annihilated: and each of the cases subdivides 
into results of good, and results of evil. What is to be 
done? 

"Periculosum est credere et non credere; 
Hippolitus obiit quia novercae creditum est; 
Cassandrse quia non creditum ruit Ilium: 
Ergo exploranda est veritas multum prius 
Quam stulta prove judicet sententia." 6 

Nova Demonstratio immobilitatis terrse petita ex virtute mag- 
netica. By Jacobus Grandamicus. Flexiae (La Fleche), 1645, 
4to. 7 

No magnetic body can move about its poles: the earth 
is a magnetic body, therefore, etc. The iron and its mag- 
netism are typical of two natures in one person; so it is 
said, "Si exaltatus fuero a terra, omnia traham ad me ip- 
sum." 8 

A VENETIAN BUDGET OF PARADOXES. 

Le glorie degli incogniti, o vero gli huomini illustri dell' acca- 
demia de' signori incogniti di Venetia. Venice, 1647, 4to. 

This work is somewhat like a part of my own: it is a 
budget of Venetian nobodies who wished to be somebodies ; 
but paradox is not the only means employed. It is of a 
serio-comic character, gives genuine portraits in copper- 
plate, and grave lists of works ; but satirical accounts. The 
astrologer Andrew Argoli 1 is there, and his son; both of 
whom, with some of the others, have place in modern works 

'"Both belief and non-belief are dangerous. Hippolitus died 
because his stepmother was believed. Troy fell because Cassandra 
was not believed. Therefore the truth should be investigated long 
before foolish opinion can properly judge." (Proves probe?). 

7 Jacobus Grandamicus (Jacques Grandami) was born at Nantes 
in 1588 and died at Paris in 1672. He was professor of theology 
and philosophy in the Jesuit colleges at Rennes, Tours, Rouen, and 
other places. He wrote several works on astronomy. 

8 "And I, if I be lifted up from the earth, will draw all men unto 
me." John xii. 32. 

1 Andrea Argoli (1568-1657) wrote a number of works on astron- 
omy, and computed ephemerides from 1621 to 1700. 



A VENETIAN BUDGET OF PARADOXES. 105 

on biography. Argoli's discovery that logarithms facilitate 
easy processes, but increase the labor of difficult ones, is 
worth recording. 

Controversise de vera circuli mensura inter C. S. Longo- 

montanum et Jo. Pellium. 2 Amsterdam, 1647, 4to. 

Longomontanus, 3 a Danish astronomer of merit, squared 
the circle in 1644: he found out that the diameter 43 gives 
the square root of 18252 for the circumference ; which gives 
3.14185... for the ratio. Pell answered him, and being 
a kind of circulating medium, managed to engage in the 
controversy names known and unknown, as Roberval, 
Hobbes, Carcavi, Lord Charles Cavendish, Pallieur, Mer- 
senne, Tassius, Baron Wolzogen, Descartes, Cavalieri and 
Golius. 4 Among them, of course, Longomontanus was made 

8 So in the original edition of the Budget. It is Johannem 
Pellum in the original title. John Pell (1610 or 1611-1685) studied 
at Cambridge and Oxford, and was professor of mathematics at 
Amsterdam (1643-46) and Breda (1646-52). He left many manu- 
scripts but published little. His name attaches by accident to an 
interesting equation recently studied with care by Dit E. E. Whit- 
ford (New York, 1912). 

8 Christianus Longomontanus (Christen Longberg or Lumborg) 
was born in 1569 at Longberg, Jutland, and died in 1647 at Copen- 
hagen. He was an assistant of Tycho Brahe and accepted the 
diurnal while denying the orbital motion of the earth. His Cyclo- 
metria e lunulis reciproce demonstrate, appeared in 1612 under the 
name of Christen Severin, the latter being his family name. He 
wrote several other works ,pn the quadrature problem, and some 
treatises on astronomy. 

*The names are really pretty well known. Giles Persone de 
Roberval was born at Roberval near Beauvais in 1602, and died at 
Paris in 1675. He was professor of philosophy at the College Ger- 
vais at Paris, and later at the College Royal. He claimed to have 
discovered the theory of indivisibles before Cavalieri, and his work 
is set forth in his Traite des indivisibles which appeared post- 
humously in 1693. 

Hobbes (1588-1679), the political and social philosopher, lived 
a good part of his time (1610-41) in France where he was tutor to 
several young noblemen, including the Cavendishes. His Leviathan 
(1651) is said to have influenced Spinoza, Leibnitz, and Rousseau. 
His Quadratura circuli, cubatio sphaerae, duplicatio cubi. . . (London, 
1669), Rosetum geometricum. .. (London, 1671), and Lux Mathe- 
j censura doctrinae Wallisianae contra Rosetum Hobbesii (Lon- 



106 A BUDGET OF PARADOXES. 

mincemeat : but he is said to have insisted on the discovery 
in his epitaph. 5 

don, 1674) are entirely forgotten to-day. (See a further note, in- 
fra.) 

Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He 
was a member of parliament, royal librarian, and member of the 
Academic des Sciences. His attempt to prove the impossibility of 
the quadrature appeared in 1645. He was a frequent correspondent 
of Descartes. 

Cavendish (1591-1654) was Sir (not Lord) Charles. He was, 
like De Morgan himself, a bibliophile in the domain of mathematics. 
His life was one of struggle, his term as member of parliament under 
Charles I being followed by gallant service in the royal army. After 
the war he sought refuge on the continent where he met most of the 
mathematicians of his day. He left a number of manuscripts on 
mathematics, which his widow promptly disposed of for waste paper. 
If De Morgan's manuscripts had been so treated we should not have 
had his revision of his Budget of Paradoxes. 

Marin Mersenne (1588-1648), a minorite, living in the cloisters 
at Nevers and Paris, was one of the greatest Franciscan scholars. 
He edited Euclid, Apollonius, Archimedes, Theodosius, and Mene- 
laus (Paris. 1626), translated the Mechanics of Galileo into French 
(1634), wrote Harmonicorum Libri XII (1636), and Cogitata phy- 
sico-mathematica (1644), and taught theology and philosophy at 
Nevers. 

Johann Adolph Tasse (Tassius) was born in 1585 and died at 
Hamburg in 1654. He was professor of mathematics in the Gym- 
nasium at Hamburg, and wrote numerous works on astronomy, 
chronology, statics, and elementary mathematics. 

Johann Ludwig, Baron von Wolzogen, seems to have been one 
of the early Unitarians, called Fratres Polonorum because they took 
refuge in Poland. Some of his works appear in the Bibliotheca 
Fratrum Polonorum (Amsterdam, 1656). I find no one by the name 
who was contributing to mathematics at this time. 

Descartes is too well known to need mention in this connection. 

Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Gali- 
leo, and professor of mathematics at Bologna. His greatest work, 
Geometric, indivisibilibus continuorum nova quadam ratione pro- 
mota, in which he makes a noteworthy step towards the calculus, 
appeared in 1635. 

Jacob (Jacques) Golius was born at the Hague in 1596 and died 
at Leyden in 1667. His travels in Morocco and Asia Minor (1622- 
1629) gave him such knowledge of Arabic that he became professor 
of that language at Leyden. After Snell's death he became pro- 
fessor of mathematics there. He translated Arabic works on mathe- 
matics and astronomy into Latin. 

* It would be interesting to follow up these rumors, beginning 
perhaps with the tomb of Archimedes. The Ludolph van Ceulen 
story is very likely a myth. The one about Fagnano may be such. 
The Bernoulli tomb does have the spiral, however (such as it is), 
as any one may see in the cloisters at Basel to-day. 



THE CIRCULATING MEDIA OF MATHEMATICS. 107 

THE CIRCULATING MEDIA OF MATHEMATICS. 
The great circulating mediums, who wrote to everybody, 
heard from everybody, and sent extracts to everybody else, 
have been Father Mersenne, John Collins, and the late 
Professor Schumacher: all "late" no doubt, but only the 
last recent enough to be so styled. If M.C.S. should ever 
again stand for "Member of the Corresponding Society," 
it should raise an acrostic thought of the three. There is 
an allusion to Mersenne's occupation in Hobbes's reply to 
him. He wanted to give Hobbes, who was very ill at Paris, 
the Roman Eucharist: but Hobbes said, "I have settled all 
that long ago; when did you hear from Gassendi?" We 
are reminded of William's answer to Burnet. John Collins 
disseminated Newton, among others. Schumacher ought 
to have been called the postmaster-general of astronomy, 
as Collins was called the attorney-general of mathematics. 1 

'Collins (1625-1683) was secretary of the Royal Society, and 
was "a kind of register of all new improvements in mathematics." 
His office brought him into correspondence with all of the English 
scientists, and he was influential in the publication of various im- 
portant works, including Branker's translation of the algebra by 
Rhonius, with notes by Pell, which was the first work to contain the 
present English-American symbol of division. He also helped in 
the publication of editions of Archimedes and Apollonius, of Ker- 
sey's Algebra, and of the works of Wallis. His profession was that 
of accountant and civil engineer, and he wrote three unimportant 
works on mathematics (one published posthumously, and the others 
in 1652 and 1658). 

Heinrich Christian Schumacher (1780-1850) was professor of 
astronomy at Copenhagen and director of the observatory at Al- 
tona. His translation of Carnot's Geometric de position (1807) 
brought him into personal relations with Gauss, and the friendship 
was helpful to Schumacher. He was a member of many learned 
societies and had a large circle of acquaintances. He published 
numerous monographs and works on astronomy. 

Gassendi (1592-1655) might well have been included by De 
Morgan in the group, since he knew and was a friend of most of 
the important mathematicians of his day. Like Mersenne, he was a 
minorite, but he was a friend of Galileo and Kepler, and wrote a 
work under the title Institutio astronomica, juxta hypotheses Coper- 
nici, Tychonis-Brahaei et Ptolemaei (1645). He taught philosophy 
at Aix, and was later professor of mathematics at the College 
Royal at Paris. 

Burnet is the Bishop Gilbert Burnet (1643-1715) who was so 
strongly anti-Romanistic that he left England during the reign of 



108 A BUDGET OF PARADOXES. 

THE SYMPATHETIC POWDER. 

A late discourse by Sir Kenelme Digby Rendered into 

English by R. White. London, 1658, I2mo. 

On this work see Notes and Queries, 2d series, vii. 231, 
299, 445, viii. 190. It contains the celebrated sympathetic 
powder. I am still in much doubt as to the connection of 
Digby with this tract. 1 Without entering on the subject 
here, I observe that in Birch's History of the Royal Society, 2 
to which both Digby and White belonged, Digby, though 
he brought many things before the Society, never mentioned 
the powder, which is connected only with the names of 
Evelyn 3 and Sir Gilbert Talbot. 4 The sympathetic powder 
was that which cured by anointing the weapon with its 
salve instead of the wound. I have long been convinced 
that it was efficacious. The directions were to keep the 

James II and joined the ranks of the Prince of Orange. William 
made him bishop of Salisbury. 

1 There is some substantial basis for De Morgan's doubts as to 
the connection of that mirandula of his age, Sir Kenelm Digby 
(1603-1665), with the famous poudre de sympathie. It is true that 
he was just the one to prepare such a powder. A dilletante in 
everything, learning, war, diplomacy, religion, letters, and science, 
he was the one to exploit a fraud of this nature. He was an 
astrologer, an alchemist, and a fabricator of tales, and well did 
Henry Stubbes characterize him as "the very Pliny of our age for 
lying." He first speaks of the powder in a lecture given at Mont- 
pellier in 1658, and in the same year he published the address at 
Paris under the title: Discours fait en une celebre assemblee par le 
chevalier Digby ... .touchant la guerison de playes par la poudre de 
sympathie. The London edition referred to by De Morgan also 
came out in 1658, and several editions followed^ it in England, France, 
and Germany. But Nathaniel Highmore in his History of Genera- 
tion (1651) referred to the concoction as "Talbot's Powder" some 
years before Digby took it up. The basis seems to have been vitriol, 
and it was claimed that it would heal a wound by simply being 
applied to a bandage taken from it. 

'This work by Thomas Birch (1705-1766) came out in 1756-57. 
Birch was a voluminous writer on English history. He was a friend 
of Dr. Johnson and of Walpole, and he wrote a life of Robert Boyle. 

8 We know so much about John Evelyn (1620-1706) through the 
diary which he began at the age of eleven, that we forget his works 
on navigation and architecture. 

4 1 suppose this was the seventh Earl of Shrewsbury (1553-1616). 



HOBBES AS A MATHEMATICIAN. 109 

wound clean and cool, and to take care of diet, rubbing the 
salve on the knife or sword. 5 If we remember the dreadful 
notions upon drugs which prevailed, both as to quantity 
and quality, we shall readily see that any way of not dressing 
the wound would have been useful. If the physicians had 
taken the hint, had been careful of diet etc., and had poured 
the little barrels of medicine down the throat of a practicable 
doll, they would have had their magical cures as well as the 
surgeons. 8 Matters are much improved now; the quantity 
of medicine given, even by orthodox physicians, would have 
been called infinitesimal by their professional ancestors. Ac- 
cordingly, the College of Physicians has a right to abandon 
its motto, which is Ars longa, vita brevis, meaning Practice 
is long, so life is short. 

HOBBES AS A MATHEMATICIAN. 

Examinatio et emendatio Mathematicae Hodiernse. By Thomas 
Hobbes. London, 1666, 4to. 

In six dialogues: the sixth contains a quadrature of the 
circle. 1 But there is another edition of this work, without 
place or date on the title-page, in which the quadrature is 
omitted. This seems to be connected with the publication 

5 This is interesting in view of the modern aseptic practice of 
surgery and the antiseptic treatment of wounds inaugurated by 
the late Lord Lister. 

6 Perhaps De Morgan had not heard the ban mot of Dr. Holmes : 
"I firmly believe that if the whole materia medica could be sunk to 
the bottom of the sea, it would be all the better for mankind and 
all the worse for the fishes." 

1 The full title is worth giving, because it shows the mathematical 
interests of Hobbes, and the nature of the six dialogues : Examina- 
tio et emendatio^ mathematicae hodiernae qualis explicatur in libris 
Johannis Wallisii geometriae professoris Saviliani in Academia Oxo- 
niensi: distributa in sex dialogos (i. De mathematicae origine...; 
2. De principiis traditis ab Euclide; 3. De demonstratione operationum 
arithmeticarum. . . ; 4. De rationibus; $.De angula contactus, de sec- 
tionibus coni, et arithmetica infinitorum; 6. Dimensio circuli tribus 
methodis demonstrata. . .item cycloidis verae descriptio et proprie- 
tates aliquot.') Londini, 1660 (not 1666). For a full discussion of 
the controversy over the circle, see George Croom Robertson's biog- 
raphy of Hobbes in the eleventh edition of the Encyclopaedia Britan- 
nica. 



110 A BUDGET OF PARADOXES. 

of another quadrature, without date, but about 1670, as 
may be judged from its professing to answer a tract of 
Wallis, printed in 1669. 2 The title is "Quadrature circuli 
cubatio sphserse, duplicatio cubi," 4to. 8 Hobbes, who began 
in 1655, was very wrong in his quadrature; but, though 
not a Gregory St. Vincent, 4 he was not the ignoramus in 
geometry that he is sometimes supposed. His writings, 
erroneous as they are in many things, contain acute remarks 
on points of principle. He is wronged by being coupled 
with Joseph Scaliger, as the two great instances of men of 
letters who have come into geometry to help the mathemati- 
cians out of their difficulty. I have never seen Scaliger's quad- 
rature, 5 except in the answers of Adrianus Romanus, 6 Vieta 
and Clavius, and in the extracts of Kastner. 7 Scaliger had 
no right to such strong opponents: Erasmus or Bentley 
might just as well have tried the problem, and either would 
have done much better in any twenty minutes of his life. 8 

AN ESTIMATE OF SCALIGER. 

Scaliger inspired some mathematicians with great respect 
for his geometrical knowledge. Vieta, the first man of his 
time, who answered him, had such regard for his opponent 

/This is his Animadversions upon Mr. Hobbes* late book De 
principiis et ratio cinatione geometrarum, 1666, or his Hobbianae 
quadraturae circuli, cubationis sphaerae et duplications cubi con- 
futatio, also of 1669. 

"This is the work of 1669 referred to above. 

4 Gregoire de St. Vincent (1584-1667) published his Opus geo- 
metricum quadraturae circuli et sectionum coni at Antwerp in 1647. 

"This appears in 7. Scaligeri cyclometrica elementa duo, Lug- 
duni Batav., 1594. 

6 Adriaen van Roomen (1561-1615) gave the value of if to sixteen 
decimal places in his Ideae mathematicae pars prima (1593), and 
wrote his In Ar chime dis circuli dimensionem expositio & analysis in 
1597- 

T Kastner. See note 5 on page 43. 

8 Bentley (1662-1742) might have done it, for as the head of Trin- 
ity College, Cambridge, and a follower of Newton, he knew some 
mathematics. Erasmus (1466-1536) lived a little too early to at- 
tempt it, although his brilliant satire might have been used to good 
advantage against those who did try. 



AN ESTIMATE OF SCALIGER. Ill 

as made him conceal Scaliger's name. Not that he is very 
respectful in his manner of proceeding: the following dry 
quiz on his opponent's logic must have been very cutting, 
being true. "In grammaticis, dare navibus Austros, et dare 
naves Austris, sunt seque significantia. Sed in Geometricis, 
aliud est adsumpsisse circulum BCD non esse majorem tri- 
ginta sex segmentis BCDF, aliud circulo BCD non esse majora 
triginta sex segmenta BCDF. Ilia adsumptiuncula vera est, 
hsec falsa." 1 Isaac Casaubon, 2 in one of his letters to De 
Thou, 3 relates that, he and another paying a visit to Vieta, 
the conversation fell upon Scaliger, of whom the host said 
that he believed Scaliger was the only man who perfectly 
understood mathematical writers, especially the Greek ones : 
and that he thought more of Scaliger when wrong than of 
many others when right ; "pluris se Scaligerum vel erran- 
tem facere quam multos KaTopOovvras"* This must have been 
before Scaliger's quadrature (1594). There is an old story 
of some one saying, "Mallem cum Scaligero errare, quam 
cum Clavio recte sapere." 5 This I cannot help suspecting 
to have been a version of Vieta's speech with Clavius satir- 
ically inserted, on account of the great hostility which Vieta 
showed towards Clavius in the latter years of his life. 

Montucla could not have read with care either Scaliger's 
quadrature or Clavius's refutation. He gives the first a 
wrong date: he assures the world that there is no question 
about Scaliger's quadrature being wrong, in the eyes of 
geometers at least : and he states that Clavius mortified him 

1 "In grammar, to give the winds to the ships and to give the ships 
to the winds mean the same thing. But in geometry it is one thing 
to assume the circle BCD not greater than thirty-six segments 
BCDF, and another (to assume) the thirty-six segments BCDF not 
greater than the circle. The one assumption is true, the other false." 

3 The Greek scholar (1559-1614) who edited a Greek and Latin 
edition of Aristotle in 1590. 

'Jacques Auguste de Thou (1553-1617), the historian and states- 
man. 

' "To value Scaliger higher even when wrong, than the multitude 
when right." 

5 "I would rather err with Scaliger than be right with Clavius." 



112 A BUDGET OF PARADOXES. 

extremely by showing that it made the circle less than its 
inscribed dodecagon, which is, of course, equivalent to as- 
serting that a straight line is not always the shortest distance 
between two points. Did Clavius show this? No, it was 
Scaliger himself who showed it, boasted of it, and declared 
it to be a "noble paradox" that a theorem false in geometry 
is true in arithmetic; a thing, he says with great triumph, 
not noticed by Archimedes himself! He says in so many 
words that the periphery of the dodecagon is greater than 
that of the circle; and that the more sides there are to the 
inscribed figure, the more does it exceed the circle in which 
it is. And here are the words, on the independent testi- 
monies of Clavius and Kastner: 

"Ambitus dodecagoni circulo inscribendi plus potest 
quam circuli ambitus. Et quanto deinceps plurium laterum 
fuerit polygonum circulo inscribendum, tanto plus poterit 
ambitus polygoni quam ambitus circuli." 6 

There is much resemblance between Joseph Scaliger 
and William Hamilton, 7 in a certain impetuousity of char- 
acter, and inaptitude to think of quantity. Scaliger main- 
tained that the arc of a circle is less than its chord in arith- 
metic, though greater in geometry; Hamilton arrived at 
two quantities which are identical, but the greater the one 
the less the other. But, on the whole, I liken Hamilton 
rather to Julius than to Joseph. On this last hero of litera- 
ture I repeat Thomas Edwards, 8 who says that a man is un- 
learned who, be his other knowledge what it may, does not 

8 " The perimeter of the dodecagon to be inscribed in a circle is 
greater than the perimeter of the circle. And the more sides a 
polygon to be inscribed in a circle successively has, so much the 
greater will the perimeter of the polygon be than the perimeter of 
the circle." 

7 De Morgan took, perhaps, the more delight in speaking thus of 
Sir William Hamilton (1788-1856) because of a spirited controversy 
that they had in 1847 over the theory of logic. Possibly, too, Sir 
William's low opinion of mathematics had its influence. 

8 Edwards (1699-1757) wrote The canons of criticism (1747) in 
which he gave a scathing burlesque on Warburton's Shakespeare. 
It went through six editions. 



JOHN GRAUNT AS A PARADOXER. 113 

understand the subject he writes about. And now one of 
many instances in which literature gives to literature char- 
acter in science. Anthony Teissier, 9 the learned annotator 
of De Thou's biographies, says of Finseus, "II se vanta 
sans raison avoir trouve la quadrature du cercle; la gloire 
de cette admirable decouverte etait reservee a Joseph Sca- 
liger, comme 1'a ecrit Scevole de St. Marthe." 10 

JOHN GRAUNT AS A PARADOXER. 

Natural and Political Observations upon the Bills of Mor- 
tality. By John Graunt, citizen of London. London, 1662, 4to. 1 

This is a celebrated book, the first great work upon mor- 
tality. But the author, going ultra crepidam, has attributed 
to the motion of the moon in her orbit all the tremors which 
she gets from a shaky telescope. 2 But there is another para- 
dox about this book : the above absurd opinion is attributed 
to that excellent mechanist, Sir William Petty, who passed 
his days among the astronomers. Graunt did not write his 
own book! Anthony Wood 3 hints that Petty "assisted, or 
put into a way" his old benefactor : no doubt the two friends 
talked the matter over many a time. Burnet and Pepys 4 
state that Petty wrote the book. It is enough for me that 

9 Antoine Teissier (born in 1632) published his Eloges des hommes 
savants, tires de I'histoire de M. de Thou in 1683. 

" He boasted without reason of having found the quadrature of 
the circle. The glory of this admirable discovery was reserved for 
Joseph Scaliger, as Scevole de St. Marthe has written." 

1 Natural and political observations mentioned in the following 

Index, and made upon the Bills of Mortality With reference to 

the government, religion, trade, growth, ayre, and diseases of the 
said city. London, 1662, 4to. The book went through several editions. 

*Ne sutor ultra crepidam, "Let the cobbler stick to his last," as 
we now say. 

8 The author (1632-1695) of the Historia et Antiquitates Universi- 
tatis Oxoniensis (1674). See note 6, page 98. 

4 The mathematical guild owes Samuel Pepys (1633-1703) for 
something besides his famous diary (1659-1669). Not ^only was he 
president of the Royal Society (1684), but he was interested in 
establishing Sir William Boreman's mathematical school at Green- 
wich. 



114 A BUDGET OF PARADOXES. 

Graunt, whose honesty was never impeached, uses the plain- 
est incidental professions of authorship throughout ; that he 
was elected into the Royal Society because he was the 
author; that Petty refers to him as author in scores of 
places, and published an edition, as editor, after Graunt's 
death, with Graunt's name of course. The note on Graunt 
in the Biographia Britannica may be consulted; it seems 
to me decisive. Mr. C. B. Hodge, an able actuary, has done 
the best that can be done on the other side in the Assurance 
Magazine, viii. 234. If I may say what is in my mind, 
without imputation of disrespect, I suspect some actuaries 
have a bias: they would rather have Petty the greater for 
their Coryphaeus than Graunt the less. 5 

Pepys is an ordinary gossip: but Burnet's account has 
an animus which is of a worse kind. He talks of "one 
Graunt, a Papist, under whose name Sir William Petty 6 
published his observations on the bills of mortality." He 
then gives the cock without a bull story of Graunt being 
a trustee of the New River Company, and shutting up the 
cocks and carrying off their keys, just before the fire of 
London, by which a supply of water was delayed. 7 It was 
one of the first objections made to Burnet's work, that 
Graunt was not a trustee at the time; and Maitland, the 
historian of London, ascertained from the books of the 
Company that he was not admitted until twenty-three days 
after the breaking out of the fire. Graunt's first admission 

"John Graunt (1620-1674) was a draper by trade, and was a 
member of the Common Council of London until he lost office by 
turning Romanist. Although a shopkeeper, he was elected to the 
Royal Society on the special recommendation of Charles II. Petty 
edited the fifth edition of his work, adding much to its size and value, 
and this may be the basis of Burnet's account of the authorship. 

Petty (1623-1687) was a mathematician and economist, and a 
friend of Pell and Sir Charles Cavendish. His survey of Ireland, 
made for Cromwell, was one of the first to be made on a large scale 
in a scientific manner. He was one of the founders of the Royal 
Society. 

T The story probably arose from Graunt's recent conversion to 
the Roman Catholic faith. 



MANKIND A GULLIBLE LOT. 115 

to the Company took place on the very day on which a com- 
mittee was appointed to inquire into the cause of the fire. 
So much for Burnet. I incline to the view that Graunt's 
setting London on fire strongly corroborates his having 
written on the bills of mortality: every practical man takes 
stock before he commences a grand operation in business. 

MANKIND A GULLIBLE LOT. 

De Cometis : or a discourse of the natures and effects of Comets, 
as they are philosophically, historically, and astrologically con- 
sidered. With a brief (yet full) account of the III late Comets, 
or blazing stars, visible to all Europe. And what (in a natural 
way of judicature) they portend. Together with some obser- 
vations on the nativity of the Grand Seignior. By John Gad- 
bury, ^iXo/cta^/AciTi/ciSs. London, 1665, 4to. 



Gadbury, though his name descends only in astrology, 
was a well-informed astronomer. 1 D'Israeli 2 sets down Gad- 
bury, Lilly, Wharton, Booker, etc., as rank rogues: I think 
him quite wrong. The easy belief in roguery and inten- 
tional imposture which prevails in educated society is, to 
my mind, a greater presumption against the honesty of 
mankind than all the roguery and imposture itself. Putting 
aside mere swindling for the sake of gain, and looking at 
speculation and paradox, I find very little reason to suspect 
wilful deceit. 3 My opinion of mankind is founded upon the 

1 He was born in 1627 and died in 1704. He published a series 
of ephemerides, beginning in 1659.- He was imprisoned in 1679, at 
the time of the "Popish Plot," and again for treason in 1690. His 
important astrological works are the Animal Cornatum, or the Horn'd 
Beast (1654) and The Nativity of the late King Charls (1659). 

3 Isaac DTsraeli (1766-1848), in his Curiosities of Literature 
(1791), speaking of Lilly, says: "I shall observe of this egregious 
astronomer, that there is in this work, so much artless narrative, 
and at the same time so much palpable imposture, that it is difficult 
to know when he is speaking what he really believes to be the truth." 
He goes on to say that Lilly relates that "those adepts whose char- 
acters he has drawn were the lowest miscreants of the town. Most 
of them had taken the air in the pillory, and others had conjured 
themselves up to the gallows. This seems a true statement of facts. 

8 It is difficult to estimate William Lilly (1602-1681) fairly. His 
Merlini Anglici ephemeris, issued annually from 1642 to 1681, brought 



116 A BUDGET OF PARADOXES. 

mournful fact that, so far as I can see, they find within 
themselves the means of believing in a thousand times as 
much as there is to believe in, judging by experience. I do 
not say anything against Isaac D'Israeli for talking his time. 
We are all in the team, and we all go the road, but we do 
not all draw. 

A FORERUNNER OF A WRITTEN ESPERANTO. 

An essay towards a real character and a philosophical language. 
By John Wilkins [Dean of Ripon, afterwards Bishop of Ches- 
ter]. 1 London, 1668, folio. 

This work is celebrated, but little known. Its object 
gives it a right to a place among paradoxes. It proposes a 
language if that be the proper name in which things 
and their relations shall be denoted by signs, not words: 
so that any person, whatever may be his mother tongue, 
may read it in his own words. This is an obvious possi- 
bility, and, I am afraid, an obvious impracticability. One 
man may construct such a system Bishop Wilkins has done 
it but where is the man who will learn it? The second 
tongue makes a language, as the second blow makes a fray. 
There has been very little curiosity about his performance, 
the work is scarce ; and I do not know where to refer the 
reader for any account of its details, except, to the partial 
reprint of Wilkins presently mentioned under 1802, in which 
there is an unsatisfactory abstract. There is nothing in the 
Biographia Britannica, except discussion of Anthony Wood's 
statement that the hint was derived from Dalgarno's book, 

him a great deal of money. Sir George Wharton (1617-1681) also 
published an almanac annually from 1641 to 1666. He tried to ex- 
pose John Booker (1603-1667) by a work entitled Mercurio-Coelicio- 
Mastix; or, an Anti-caveat to all such, as have (heretofore} had the 
misfortune to be Cheated and Deluded by that Grand and Traiterous 
Impostor of this Rebellious Age, John Booker, 1644. Booker was 
"licenser of mathematical [astrological] publications," and as such 
he had quarrels with Lilly, Wharton, and others. 

J See note i on page 100. 



GREGOIRE DE ST. VINCENT. 117 

De Signis, 1661. 2 Hamilton (Discussions, Art. 5, "Dal- 
garno") does not say a word on this point, beyond quoting 
Wood; and Hamilton, though he did now and then write 
about his countrymen with a rough-nibbed pen, knew per- 
fectly well how to protect their priorities. 

GREGOIRE DE ST. VINCENT. 

Problema Austriacum. Plus ultra Quadratura Circuli. Auctore 
P. Gregorio a Sancto Vincentio Soc. Jesu., Antwerp, 1647, 
folio. Opus Geometricum posthumum ad Mesolabium. By 
the same. Gandavi [Ghent], 1668, folio. 1 

The first book has more than 1200 pages, on all kinds of 
geometry. Gregory St. Vincent is the greatest of circle- 
squarers, and his investigations led him into many truths: 
he found the property of the area of the hyperbola 2 which \ 
led to Napier's logarithms being called hyperbolic. Mon- 
tucla says of him, with sly truth, that no one has ever 
squared the circle with so much genius, or, excepting his 
principal object, with so much success. 3 His reputation, and 
the many merits of his work, led to a sharp controversy on 
his quadrature, which ended in its complete exposure by 
Huyghens and others. He had a small school of followers, 
who defended him in print. 

2 This is the Ars Signorum, vulgo character universalis et lingua 
philosophica, that appeared at London in 1661, 8vo. George Dal- 
garno anticipated modern methods in the teaching of the deaf and 
dumb. 

1 See note 4 on page no. 

2 If the hyperbola is referred to the asymptotes as axes, the area 
between two ordinates (x-=a, x = b) is the difference of the loga- 
rithms of a and b to the base e. E. g., in the case of the hyperbola 
xy =. i, the area between x = a and x = I is log a. 

"'On ne peut lui refuser la justice de remarquer que personne 
avant lui ne s'est porte dans cette recherche ayec autant de genie, 
& meme, si nous en exceptons son objet principal, avec autant de 
succes." Quadrature du Cercle, p. 66. 



118 A BUDGET OF PARADOXES. 



RENE DE SLUSE. 

Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liege], 
1668, 410.1 

The Mesolabum is the solution of the problem of finding 
two mean proportionals, which Euclid's geometry does not 
attain. Slusius is a true geometer, and uses the ellipse, etc. : 
but he is sometimes ranked with the trisecters, for which 
reason I place him here, with this explanation. 

The finding of two mean proportionals is the prelim- 
inary to the famous old problem of the duplication of the 
cube, proposed by Apollo (not Apollonius) himself. D'ls- 
raeli speaks of the "six follies of science," the quadrature, 
the duplication, the perpetual motion, the philosopher's 
stone, magic, and astrology. He might as well have added 
the trisection, to make the mystic number seven : but had he 
done so, he would still have been very lenient; only seven 
follies in all science, from mathematics to chemistry! Sci- 
ence might have said to such a judge as convicts used to 
say who got seven years, expecting it for life, "Thank you, 
my Lord, and may you sit there till they are over," may 
the Curiosities of Literature outlive the Follies of Science! 

JAMES GREGORY. 

1668. In this year James Gregory, in his Vera Circuli 
et Hyperboles Quadratura* held himself to have proved that 

1 The title proceeds: Seu duae mediae proportionates inter ex- 
tremas datas per circulum et per infinitas hyperbolas, vel ellipses et 
per quamlibet exhibitae. . . .Rene Francois, Baron de Sluse (1622- 
1685) was canon and chancellor of Liege, and a member of the Royal 
Society. He also published a work on tangents (1672). The word 
mesolabium is from the Greek neffo\dptoi> or pecroXapov, an instru- 
ment invented by Eratosthenes for finding two mean proportionals. 

*The full title has some interest: Vera circuit et hyperbolae quad- 
ratura cui accedit geometriae^ pars universalis inserviens quantita- 
tum curvarum transmutationi et mensurae. Authore Jacobo Gre- 
gorio Abredonensi Scoto Patavii, 1667. That is, James Greg- 
ory (1638-1675) of Aberdeen (he was really born near but not in 
the city), a good Scot, was publishing his work down in Padua. 
The reason was that he had been studying in Italy, and that this 



BEAULIEU'S QUADRATURE. 1 19 

the geometrical quadrature of the circle is impossible. Few 
mathematicians read this very abstruse speculation, and 
opinion is somewhat divided. The regular circle-squarers 
attempt the arithmetical quadrature, which has long been 
proved to be impossible. Very few attempt the geometrical 
quadrature. One of the last is Malacarne, an Italian, who 
published his Solution Geometrique, at Paris, in 1825. His 
method would make the circumference less than three times 
the diameter. 

BEAULIEU'S QUADRATURE. 

La Geometric Frangoise, ou la Pratique aisee La quadracture 

du cercle. Par le Sieur de Beaulieu, Ingenieur, Geographe du 
Roi Paris, 1676, 8vo. [not Pontault de Beaulieu, the cele- 
brated topographer; he died in 1674] - 1 

If this book had been a fair specimen, I might have 
pointed to it in connection with contemporary English works, 
and made a scornful comparison. But it is not a fair speci- 
men. Beaulieu was attached to the Royal Household, and 
throughout the century it may be suspected that the house- 
hold forced a royal road to geometry. Fifty years before, 
Beaugrand, the king's secretary, made a fool of himself, 
and [so?] contrived to pass for a geometer. He had inter- 
est enough to get Desargues, the most powerful geometer 
of his time, 2 the teacher and friend of Pascal, prohibited from 

was a product of his youth. He had already (1663) published his 
Optica promota, and it is not remarkable that his brilliancy 
brought him a wide circle of friends on the continent and the offer 
of a pension from Louis XIV. He became professor of mathematics 
at St. Andrews and later at Edinburgh, and invented the first suc- 
cessful reflecting telescope. The distinctive feature of his Vera 
quadrature, is his use of an infinite converging series, a plan that 
Archimedes used with the parabola. 

1 Jean^de Beaulieu wrote several works on mathematics, including 
La lumiere de I'arithmetique (n. d.), La lumie're des mathematiques 
(1673), Nouvelle invention d'arithmetique (1677), and some mathe- 
matical tables. 

a A just estimate. There were several works published by Gerard 
Desargues (1593-1661), of which the greatest was the Brouillon 
Prole ct (Paris, 1639). There is an excellent edition of the (Euvres 
de Desargues by M. Poudra, Paris, 1864. 



120 A BUDGET OF PARADOXES. 

lecturing. See some letters on the History of Perspective, 
which I wrote in the Athen&um, in October and November, 
1861. Montucla, who does not seem to know the true secret 
of Beaugrand's greatness, describes him as "un certain M. 
de Beaugrand, mathematicien, fort mal traite par Descartes, 
et a ce qu'il paroit avec justice." 3 

Beaulieu's quadrature amounts to a geometrical con- 
struction* which gives Tr=\/I0. His depth may be ascer- 
tained from the following extracts. First on Copernicus: 

"Copernic, Allemand, ne s'est pas moins rendu illustre 
par ses doctes ecrits; et nous pourrions dire de luy, qu'il 
seroit le seul et unique en la force de ses Problemes, si sa 
trop grande presomption ne Tavoit porte a avancer en cette 
Science une proposition aussi absurde, qu'elle est contre la 
Foy et raison, en faisant la circonference d'un Cercle fixe, 
immobile, et le centre mobile, sur lequel principe Geome- 
trique, il a avance en son Traitte Astrologique le Soleil fixe, 
et la Terre mobile." 5 

I digress here to point out that though our quadrators, 
etc., very often, and our historians sometimes, assert that 
men of the character of Copernicus, etc., were treated with 
contempt and abuse until their day of ascendancy came, 
nothing can be more incorrect. From Tycho Brahe 6 to 
Beaulieu, there is but one expression of admiration for the 
genius of Copernicus. There is an exception, which, I 

8 "A certain M. de Beaugrand, a mathematician, very badly treated 
by Descartes, and, as it appears, rightly so." 

*This is a very old approximation for IT. One of the latest pre- 
tended geometric proofs resulting in this value appeared in New 
York in 1910, entitled Quadrimetry (privately printed). 

5 "Copernicus, a German, made himself no less illustrious by his 
learned writings ; and we might say of him that he stood alone and 
unique in the strength of his problems, if his excessive presumption 
had not led him to set forth in this science a proposition so absurd 
that it is contrary to faith and reason, namely that the circumference 
of a circle is fixed and immovable while the center is movable; on 
which geometrical principle he has declared in his astrological treat- 
ise that the sun is fixed and the earth is in motion." 

6 So in the original. 



BEAULIEU'S QUADRATURE. 121 

believe, has been quite misunderstood. Maurolycus, 7 in his 
De Sphara, written many years before its posthumous pub- 
lication in 1575, and which it is not certain he would have 
published, speaking of the safety with which various authors 
may be read after his cautions, says, "Toleratur et Nicolaus 
Copernicus qui Solem fixum et Terram in girum circumverti 
posuit: et scutica potius, aut flagello, quam reprehensione 
dignus est." s Maurolycus was a mild and somewhat con- 
temptuous satirist, when expressing disapproval: as we 
should now say, he pooh-poohed his opponents ; but, unless 
the above be an instance, he was never savage nor impetuous. 
I am fully satisfied that the meaning of the sentence is, that 
Copernicus, who turned the earth like a boy's top, ought 
rather to have a whip given him wherewith to keep up his 
plaything than a serious refutation. To speak of tolerating 
a person as being more worthy of a flogging than an argu- 
ment, is almost a contradiction. 

I will now extract Beaulieu's treatise on algebra, entire. 

"L'Algebre est la science curieuse des Sgavans et speciale- 
ment d'un General d'Armee ou Capitaine, pour promptement 
ranger une Armee en bataille, et nombre de Mousquetaires 
et Piquiers qui composent les bataillons d'icelle, outre les 
figures de 1'Arithmetique. Cette science a 5 figures par- 
ticulieres en cette sorte. P signifie plus au commerce, et 
a TArmee Piquiers. M signifie moins, et Mousquetaire en 
1'Art des bataillons. [It is quite true that P and M were 
used for plus and minus in a great many old works.] R 
signifie racine en la mesure du Cube, et en TArmee rang. Q 
signifie quare en 1'un et Tautre usage. C signifie cube en 
la mesure, et Cavallerie en la composition des bataillons et 
escadrons. Quant a Toperation de cette science, c'est d'ad- 

7 Franciscus Maurolycus (1494-1575) was really the best mathe- 
matician produced by Sicily for a long period. He made Latin trans- 
lations of Theodosius, Menelaus, Euclid, Apollonius, and Archi- 
medes, and wrote on cosmography and other mathematical subjects. 

8 "Nicolaus Copernicus is also tolerated who asserted that the sun 
is fixed and that the earth whirls about it ; and he rather deserves a 
whip or a lash than a reproof." 



122 A BUDGET OF PARADOXES. 

ditionner un plus d'avec plus, la somme sera plus, et moins 
d'avec plus, on soustrait le moindre du plus, et la reste est 
la somme requise ou nombre trouve. Je dis settlement cecy 
en passant pour ceux qui n'en sgavent rien du tout." 9 

This is the algebra of the Royal Household, seventy- 
three years after the death of Vieta. Quaere, is it possible 
that the fame of Vieta, who himself held very high stations 
in the household all his life, could have given people the 
notion that when such an officer chose to declare himself 
an algebraist, he must be one indeed? This would explain 
Beaugrand, Beaulieu, and all the beaux. Beaugrand not 
only secretary to the king, but "mathematician" to the Duke 
of Orleans I wonder what his "fool" could have been like, 
if indeed he kept the offices separate, would have been in 
my list if I had possessed his Geostatique, published about 
1638. 10 He makes bodies diminish in weight as they approach 
the earth, because the effect of a weight on a lever is less 
as it approaches the fulcrum. 

""Algebra is the curious science of scholars, and particularly for 
a general of an army, or a captain, in order quickly to draw up an 
army in battle array and to number the musketeers and pikemen 
who compose it, without the figures of arithmetic. This science 
has five special figures of this kind: P means plus in commerce and 
pikemen in the army; M means minus, and musketeer in the art of 
war;. . . .R signifies root in the measurement of a cube, and rank in 
the army, Q means square (French quare, as then spelled) in both 
cases; C means cube in mensuration, and cavalry in arranging ba- 
tallions and squadrons. As for the operations of this science, they 
are as follows : to add a plus and a plus, the sum will be plus-, to add 
minus with plus, take the less from the greater and the remainder 
will be the sum required or the number to be found. I say this only in 
passing, for the benefit of those who are wholly ignorant of it." 

10 He refers to the Joannis de Beaugrand Geostatice, seu de 

vario ponder e graviitm secundum varia a terrae (centro) intervalla 
dissertatio mathematica, Paris, 1636. Pascal relates that de Beau- 
grand sent all of Roberval's theorems on the cycloid and Fermat s 
on maxima and minima to Galileo in 1638, pretending that they were 
his own. 



SIR MATTHEW HALE. 123 



SIR MATTHEW HALE. 

Remarks upon two late ingenious discourses By Dr. Henry 

More. 1 London, 1676, 8vo. 

In 1673 and 1675, Matthew Hale, 2 then Chief Justice, 
published two tracts, an "Essay touching Gravitation," and 
"Difficiles Nugae" on the Torricellian experiment. Here 
are the answers by the learned and voluminous Henry 
More. The whole would be useful to any one engaged in 
research about ante-Newtonian notions of gravitation. 

Observations touching the principles of natural motions; and 
especially touching rarefaction and condensation. .. .By the 
author of Difficiles Nuga. London, 1677, 8vo. 

This is another tract of Chief Justice Hale, published 
the year after his death. The reader will remember that 
motion, in old philosophy, meant any change from state to 
state: what we now describe as motion was local motion. 
This is a very philosophical book, about flux and materia 
prima, virtus activa and essentialis, and other fundamentals. 
I think Stephen Hales, the author of the "Vegetable Statics," 
has the writings of the Chief Justice sometimes attributed 
to him, which is very puny justice indeed. 3 Matthew Hale 
died in 1676, and from his devotion to science it probably 
arose that his famous Pleas of the Crown* and other law 
works did not appear until after his death. One of his 

1 More (1614-1687) was a theologian, a fellow of Christ College, 
Cambridge, and a Christian Platonist. 

2 Matthew Hale (1609-1676) the famous jurist, wrote a number 
of tracts on scientific, moral, and religious subjects. These were 
collected and published in 1805. 

3 They might have been attributed to many a worse man than Dr. 
Hales (1677-1761), who was a member of the Royal Society and of 
the Paris Academy, and whose scheme for the ventilation of prisons 
reduced the mortality at the Savoy prison from one hundred to only 
four a year. The book to which reference is made is Vegetable 
Staticks or an Account of some statical experiments on the sap in 
Vegetables, 1727. 

* Pleas of the Crown; or a Methodical Summary of the Principal 
Matters relating to the subject, 1678. 



124 A BUDGET OF PARADOXES. 

contemporaries was the astronomer Thomas Street, whose 
Caroline Tables 5 were several times printed: another con- 
temporary was his brother judge, Sir Thomas Street. 6 But 
of the astronomer absolutely nothing is known: it is very 
unlikely that he and the judge were the same person, but 
there is not a bit of positive evidence either for or against, 
so far as can be ascertained. Halley 7 no less a person 
published two editions of the Caroline Tables, no doubt 
after the death of the author: strange indeed that neither 
Halley nor any one else should leave evidence that Street 
was born or died. 

Matthew Hale gave rise to an instance of the lengths 
a lawyer will go when before a jury who cannot detect him. 
Sir Samuel Shepherd, 8 the Attorney General, in opening 
Hone's 9 first trial, calls him "one who was the most learned 
man that ever adorned the Bench, the most even man 
that ever blessed domestic life, the most eminent man that 
ever advanced the progress of science, and one of the 
[very moderate] best and most purely religious men that 
ever lived." 



B Thomae Streete Astronomia Carolina, a new theory of the celes- 
tial motions, 1661. It also appeared at Nuremberg in 1705, and at 
London in 1710 and 1716 ( Halley' s editions). He wrote other works 
on astronomy. 

8 This was the Sir Thomas Street (1626-1696) who passed sen- 
tence of death on a Roman Catholic priest for saying mass. The 
priest was reprieved by the king, but in the light of the present day 
one would think the justice more in need of pardon. He took part 
in the trial of the Rye House Conspirators in 1683. 

'Edmund Halley (1656-1742), who succeeded Wallis (1703) as 
Savilian professor of mathematics at Oxford, and Flamsteed (1720) 
as head of the Greenwich observatory. It is^ of interest to note that 
he was instrumental in getting Newton's Principia printed. 

8 Shepherd (born in 1760) was one of the most famous lawyers 
of his day. He was knighted in 1814 and became Attorney General 
in 1817. 

"This was William Hone (1780-1842), a book publisher, who 
wrote satires against the government, and who was tried three 
times because of his parodies on the catechism, creed, and litany 
(illustrated by Cruikshank). He was acquitted on all of the charges. 



ON THE DISCOVERY OF ANTIMONY. 125 



ON THE DISCOVERY OF ANTIMONY. 

Basil Valentine his triumphant Chariot of Antimony, with an- 
notations of Theodore Kirkringius, M.D. With the true book 
of the learned Synesius, a Greek abbot, taken out of the Em- 
perour's library, concerning the Philosopher's Stone. Lon- 
don, 1678, Svo. 1 

There are said to be three Hamburg editions of the col- 
lected works of Valentine, who discovered the common 
antimony, and is said to have given the name antimoine, 
in a curious way. Finding that the pigs of his convent 
throve upon it, he gave it to his brethren, who died of it. 2 
The impulse given to chemistry by R. Boyle 3 seems to 
have brought out a vast number of translations, as in the 
following tract: 

ON ALCHEMY. 

Collectanea Chymica : A collection of ten several treatises in 
chymistry, concerning the liquor Alkehest, the Mercury of 
Philosophers, and other curiosities worthy the perusal. Writ- 
ten by Eir. Philaletha, 1 Anonymus, J. B. Van-Helmont, 2 Dr. Fr. 

1 Valenlinus was a Benedictine monk and was still living at Erfurt 
in 1413. His Currus triumphalis antimonii appeared in 1624. Syne- 
sius was Bishop of Ptolemaide, who died about 430. His works 
were printed at Paris in 1605. Theodor Kirckring (1640-1693) was 
a fellow-student of Spinoza's. Besides the commentary on Valen- 
tine he left several works on anatomy. His commentary appeared at 
Amsterdam in 1671. There were several editions of the Chariot. 

2 The chief difficulty with this curious "monk-bane" etymology is 
its absurdity. The real origin of the word has given etymologists 
a good deal of trouble. 

"Robert Boyle (1627-1691), son of "the Great Earl" (of Cork). 
Perhaps his best-known discovery is the law concerning the volume 
of gases. 

1 The real name of Eirenaeus Philalethes (born in 1622) is un- 
known. It may have been Childe. He claimed to have discovered 
the philosopher's stone in 1645. His tract in this work is The Secret 
of the Immortal Liquor Alkahest or Ignis- A qua. See note 7, infra. 

"Johann Baptist van Helmont, Herr von Merode, Royenborg 
etc. (1577-1644). His chemical discoveries appeared in his Ortus 
medicinae (1648), which went through many editions. 



126 A BUDGET OF PARADOXES. 

Antonie, 3 Bernhard Earl of Trevisan, 4 Sir Geo. Ripley, 5 Rog. 
Bacon, 6 Geo. Starkie, 7 Sir Hugh Platt, 8 and the Tomb of Sem- 
iramis. See more in the contents. London, 1684, 8vo. 

In the advertisements at the ends of these tracts there 
are upwards of a hundred English tracts, nearly all of the 
period, and most of them translations. Alchemy looks up 
since the chemists have found perfectly different substances 
composed of the same elements and proportions. It is true 
the chemists cannot yet transmute', but they may in time: 
they poke about most assiduously. It seems, then, that the 
conviction that alchemy must be impossible was a delusion : 
but we do not mention it. 

8 De Morgan should have written up Francis Anthony (1550-1623), 
whose Panacea aurea sive tractatus duo de auro potabili (Hamburg, 
1619) described a panacea that he gave for every ill. He was re- 
peatedly imprisoned for practicing medicine without a license from 
the Royal College of Physicians. 

4 Bernardus Trevisanus (1406-1490), who traveled even through 
Barbary, Egypt, Palestine, and Persia in search of the philosopher's 
stone. He wrote several works on alchemy, De Chemica (1567), 
De Chemico Miraculo (1583), Trait e de la nature de I'oeuf des phi- 
losophes (1659), etc., all published long after his death. 

"George Ripley (1415-1490) was an Augustinian monk, later a 
chamberlain of Innocent VIII, and still later a Carmelite monk. 
His Liber de mercuris philosophico and other tracts first appeared 
in Opuscula quaedam chymica (Frankfort, 1614). 

6 Besides the Opus majus, and other of the better known works 
of this celebrated Franciscan (1214-1294), there are numerous tracts 
on alchemy that appeared in the Thesaurus chymicus (Frankfort, 
1603). 

7 George Starkey (1606-1665 or 1666) has special interest for 
American readers. He seems to have been born in the Bermudas 
and to have obtained the bachelor's degree in England. He then 
went to America and in 1646 obtained the master's degree at Har- 
vard, apparently under the name of Stirk. He met Eirenaeus Phila- 
lethes (see note I above) in America and learned alchemy from 
him. Returning to England, he sold quack medicines there, and 
died in 1666 from the plague after dissecting a patient who had 
died of the disease. Among his works was the Liquor Alcahest, or 
a Discourse of that Immortal Dissolvent of Paracelsus and Helmont, 
which appeared (1675) some nine years after his death. 

8 Platt (1552-1611) was the son of a London brewer. Although 
he left a manuscript on alchemy, and wrote a book entitled Delights 
for Ladies to adorne their Persons (1607), he was knighted for 
some serious work on the chemistry of agriculture, fertilizing, brew- 
ing, and the preserving of foods, published in The Jewell House of 
Art and Nature (1594). 



ON ALCHEMY. 127 

The astrologers and the alchemists caught it in company 
in the following, of which I have an unreferenced note. 

"Mendacem et futilem hominem nominare qui volunt, 
calendariographum dicunt; at qui sceleratum simul ac im- 
postorem, chimicum. 9 

"Crede ratem ventis corpus ne crede chimistis ; 
Est qusevis chimica tutior aura fide." 10 

Among the smaller paradoxes of the day is that of the 
Times newspaper, which always spells it chymistry: but so, 
I believe, do Johnson, Walker, and others. The Arabic 
work is very likely formed from the Greek: but it may be 
connected either with x r ll ji * la or w ^ tn 



Lettre d'un gentil-homme de province a une dame de qualite, 
sur le sujet de la Comete. Paris, 1681, 4to. 

An opponent of astrology, whom I strongly suspect to 
have been one of the members of the Academy of Sciences 
under the name of a country gentleman, 11 writes very good 
sense on the tremors excited by comets. 

The Petitioning-Comet : or a brief Chronology of all the famous 
Comets and their events, that have happened from the birth of 
Christ to this very day. Together with a modest enquiry into 
this present comet, London, 1681, 4to. 

A satirical tract against the cometic prophecy: 
"This present comet (it's true) is of a menacing aspect, 
but if the new parliament (for whose convention so many 
good men pray) continue long to sit, I fear not but the star 
will lose its virulence and malignancy, or at least its portent 
be averted from this our nation ; which being the humble 
request to God of all good men, makes me thus entitle it, 
a Petitioning-Comet." 

' "Those who wish to call a man a liar and deceiver speak of him 
as a writer of almanacs; but those who (would call him) a scoun- 
drel and an imposter (speak of him as) a chemist." 

1 "Trust your barque to the winds but not your body to a chem- 
ist ; any breeze is safer than the faith of a chemist." 

"Probably the Jesuit, Pere Claude Frangois Menestrier (1631- 
1705)5 a well-known historian. 



128 A BUDGET OF PARADOXES. 

The following anecdote is new to me : 

"Queen Elizabeth (1558) being then at Richmond, and 
being disswaded from looking on a comet which did then 
appear, made answer, jacta est alea, the dice are thrown; 
thereby intimating that the pre-order'd providence of God 
was above the influence of any star or comet." 

The argument was worth nothing: for the comet might 
have been on the dice with the event; the astrologers said 
no more, at least the more rational ones, who were about 
half of the whole. 

An astrological and theological discourse upon this present 
great conjunction (the like whereof hath not (likely) been in 
some ages) ushered in by a great comet. London, 1682, 4to. 
By C. N.i2 

The author foretells the approaching "sabbatical jubilee," 
but will not fix the date: he recounts the failures of his 
predecessors. 

A judgment of the comet which became first generally visible 
to us in Dublin, December 13, about 15 minutes before 5 in 
the evening, A. D. 1680. By a person of quality. Dublin, 1682, 
4to. 

The author argues against cometic astrology with great 
ability. 

A prophecy on the conjunction of Saturn and Jupiter in this 
present year 1682 . With some prophetical predictions of what 
is likely to ensue therefrom in the year 1684. By John Case, 
Student in physic and astrology. 13 London, 1682, 4to. 

"The author was Christopher Nesse (1621-1705), a belligerent 
Calvinist, who wrote many controversial works and succeeded in 
getting excommunicated four times. One of his most virulent works 
was A Protestant Antidote against the Poison of Popery. 

M John Case (c. 1660-1700) was a famous astrologer and physician. 
He succeeded to Lilly's practice in London. In a darkened room, 
wherein he kept an array of mystical apparatus, he pretended to 
show the credulous the ghosts of their departed relatives. Besides 
his astrological works he wrote one serious treatise, the Compendium 
Anatomicum nova methodo insiitutum (1695), m which he defends 
Harvey^s theories of embryology. 



MATHEMATICAL THEOLOGY. 129 

According to this writer, great conjunctions of Jupiter 
and Saturn occur "in the fiery trigon," about once in 800 
years. Of these there are to be seven : six happened in the 
several times of Enoch, Noah, Moses, Solomon, Christ, 
Charlemagne. The seventh, which is to happen at "the 
lamb's marriage with the bride," seems to be that of 1682 ; 
but this is only vaguely hinted. 

De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 

1698, 4to. 
Ampliatie en demonstratie wegens de Quadrature. .. .By Jacob 

Marcelis. Amsterdam, 1699, 4to. 
Eenvoudig vertoog briev-wys geschrevem am J. Marcelis 

Amsterdam, 1702, 4to. 
De sleutel en openinge van de quadrature Amsterdam, 1704, 

4to. 

Who shall contradict Jacob Marcelis ? 14 He says the cir- 
cumference contains the diameter exactly times 

~ 1008449087377541679894282184894 
6997183637540819440035239271702 

But he does not come very near, as the young arithmetician 
will find. 

MATHEMATICAL THEOLOGY. 

Theologiae Christianae Principia Mathematica. Auctore Johanne 
Craig. 1 London, 1699, 4to. 

This is a celebrated speculation, and has been reprinted 
abroad, and seriously answered. Craig is known in the 
early history of fluxions, and was a good mathematician. 

"Marcelis (1636 after 1714) was a soap maker of Amsterdam. 
It is to be hoped that he made better soap than values of n\ 

*John Craig (died in 1731) was a Scotchman, but most of his 
life was spent at Cambridge reading and writing on mathematics. 
He endeavored to introduce the Leibnitz differential calculus into 
England. His mathematical works include the Methodus Figurarum 
. . . Quadraturas dcterminandi ( 1685) , Tractatus. . . de Figurarum Cur- 
vilincarum Quadratures et locis Geometricis (1693), andDeCalculo 
Flucntium libri duo (1718). 



130 A BUDGET OF PARADOXES. 

He professed to calculate, on the hypothesis that the sus- 
picions against historical evidence increase with the square 
of the time, how long it will take the evidence of Chris- 
tianity to die out. He finds, by formulae, that had it been 
oral only, it would have gone out A. D. 800 ; but, by aid of 
the written evidence, it will last till A. D. 3150. At this 
period he places the second coming, which is deferred until 
the extinction of evidence, on the authority of the question 
"When the Son of Man cometh, shall he find faith on the 
earth?" It is a pity that Craig's theory was not adopted: 
it would have spared a hundred treatises on the end of the 
world, founded on no better knowledge than his, and many 
of them falsified by the event. The most recent (October, 
1863) is a tract in proof of Louis Napoleon being Anti- 
christ, the Beast, the eighth Head, etc. ; and the present dis- 
pensation is to close soon after 1864. 

In order rightly to judge Craig, who added speculations 
on the variations of pleasure and pain treated as functions 
of time, it is necessary to remember that in Newton's day 
the idea of force, as a quantity to be measured, and as 
following a law of variation, was very new: so likewise 
was that of probability, or belief, as an object of measure- 
ment. 2 The success of the Principia of Newton put it into 
many heads to speculate about applying notions of quantity 
to other things not then brought under measurement. Craig 
imitated Newton's title, and evidently thought he was mak- 
ing a step in advance: but it is not every one who can 
plough with Samson's heifer. 

It is likely enough that Craig took a hint, directly or 
indirectly, from Mohammedan writers, who make a reply 
to the argument that the Koran has not the evidence derived 

2 As is well known, this subject owes much to the Bernoullis. 
Craig's works on the calculus brought him into controversy with 
them. He also wrote on other subjects in which they were interested, 
as in his memoir On the Curve of the quickest descent (1700), On the 
Solid of least resistance (1700), and the Solution of Bernoulli's 
problem on Curves (1704). 



THE ARISTOCRAT AS A SCIENTIST. 131 

from miracles. They say that, as evidence of Christian 
miracles is daily becoming weaker, a time must at last arrive 
when it will fail of affording assurance that they were mir- 
acles at all: whence would arise the necessity of another 
prophet and other miracles. Lee, s the Cambridge Orientalist, 
from whom the above words are taken, almost certainly 
never heard of Craig or his theory. 

THE ARISTOCRAT AS A SCIENTIST. 

Copernicans of all sorts convicted. . . .to which is added a Treat- 
ise of the Magnet. By the Hon. Edw. Howard, of Berks. 
London, 1705, 8vo. 

Not all the blood of all the Howards will gain respect 
for a writer who maintains that eclipses admit no possible 
explanation under the Copernican hypothesis, and who asks 
how a man can "go 200 yards to any place if the moving 
superficies of the earth does carry it from him?" Horace 
Walpole, at the beginning of his Royal and Noble Authors, 
has mottoed his book with the Cardinal's address to Ariosto, 
"Dove diavolo, Messer Ludovico, avete pigliato tante co- 
glionerie?" 1 Walter Scott says you could hardly pick out, 
on any principle of selection except badness itself, he 
means of course the same number of plebeian authors 
whose works are so bad. But his implied satire on aristo- 
cratic writing forgets two points. First, during a large 
period of our history, when persons of rank condescended 
to write, they veiled themselves under "a person of honor," 
"a person of quality," and the like, when not wholly un- 
described. Not one of these has Walpole got; he omits, 

8 This is Samuel Lee (1783-1852), the young prodigy in lan- 
guages. He was apprenticed to a carpenter at twelve and learned 
Greek while working at the trade. Before he was twenty-five he 
knew Hebrew, Chaldee, Syriac, Samaritan, Persian, and Hindustani. 
He later became Regius professor of Hebrew at Cambridge. 

1 "Where the devil, Master Ludovico, did you pick up such a 

collection ?" 



132 A BUDGET OF PARADOXES. 

for instance, Lord Brounker's 2 translation of Descartes on 
Music. Secondly, Walpole only takes the heads of houses: 
this cuts both ways; he equally eliminates the Hon. Robert 
Boyle and the precious Edward Howard. The last writer is 
hardly out of the time in which aristocracy suppressed its 
names; the avowal was then usually meant to make the 
author's greatness useful to the book. In our day, literary 
peers and honorables are very favorably known, and con- 
tain an eminent class. 3 They rough it like others, and if 
such a specimen as Edw. Howard were now to appear, he 
would be greeted with 

"Hereditary noodle ! knowest thou not 
Who would be wise, himself must make him so?" 

THE LONGITUDE PROBLEM. 

A new and easy method to find the longitude at land or sea. 
London, 1710, 4to. 

This tract is a little earlier than the great epoch of such 
publications (1714), and professes to find the longitude by 
the observed altitudes of the moon and two stars, 1 

2 Lord William Brounker (c. 1620-1684), the first president of 
the Royal Society, is best known in mathematics for his contribu- 
tions to continued fractions. 

"Horace Walpole (1717-1797) published his Catalogue of the 
Royal and Noble Authors of England in 1758. Since his time a 
number of worthy names in the domain of science in general and of 
mathematics in particular might be added from the peerage of 
England. 

*It was written by Charles Hayes (1678-1760), a mathematician 
and scholar of no mean attainments. He travelled extensively, and 
was deputy governor of the Royal African Company. His Treatise 
on Fluxions (London, 1704) was the first work in English to ex- 
plain Newton's calculus. He wrote a work entitled The Moon 
(1723) to prove that our satellite shines by its own as well as by 
reflected light. His Chronographia Asiatica & Aegyptica (1758) 
gives the results of his travels. 



THE LONGITUDE PROBLEM. 133 

A new method for discovering the longitude both at sea and 
land, humbly proposed to the consideration of the public. 2 By 
Wm. Whiston 3 and Humphry Ditton. 4 London, 1714, 8vo. 

This is the celebrated tract, written by the two Arian 
heretics. Swift, whose orthodoxy was as undoubted as his 
meekness, wrote upon it the epigram if, indeed, that be 
epigram of which the point is pious wish which has been 
so often recited for the purity of its style, a purity which 
transcends modern printing. Perhaps some readers may 
think that Swift cared little for Whiston and Ditton, except 
as a chance hearing of their plan pointed them out as good 
marks. But it was not so: the clique had their eye on the 
guilty pair before the publication of the tract. The preface 
is dated July 7 ; and ten days afterwards Arbuthnot 5 writes 
as follows to Swift: 

"Whiston has at last published his project of the longi- 
tude; the most ridiculous thing that ever was thought on. 
But a pox on him! he has spoiled one of my papers of 
Scriblerus, which was a proposition for the longitude not 
very unlike his, to this purpose; that since there was no 
pole for east and west, that all the princes of Europe should 
join and build two prodigious poles, upon high mountains, 

"Publick in the original. 

8 Whiston (1667-1752) succeeded Newton as Lucasian professor 
of mathematics at Cambridge. In 1710 he turned Arian and was 
expelled from the university. His work on Primitive Christianity 
appeared the following year. He wrote many works on astronomy 
and religion. 

* Ditton (1675-1715) was, on Newton's recommendation, made 
head of the mathematical school at Christ's Hospital, London. He 
wrote a work on fluxions (1706). His idea for rinding longitude 
at sea was to place stations in the Atlantic to fire off bombs at regu- 
lar intervals, the time between the sound and the flash giving the 
distance. He also corresponded with Huyghens concerning the 
use of chronometers for the purpose. 

5 This was John Arbuthnot (c. 1658-1735), the mathematician, 
physician and wit. He was intimate with Pope and Swift, and 
was Royal physician to Queen Anne. Besides various satires he 
published a translation of Huyghens's work on probabilities (1692) 
and a well-known treatise on ancient coins, weights, and measures 
(1727). 



134 A BUDGET OF PARADOXES. 

with a vast lighthouse to serve for a polestar. I was think- 
ing of a calculation of the time, charges, and dimensions. 
Now you must understand his project is by lighthouses, 
and explosion of bombs at a certain hour." 

The plan was certainly impracticable; but Whiston and 
Ditton might have retorted that they were nearer to the 
longitude than their satirist to the kingdom of heaven, or 
even to a bishopric. Arbuthnot, I think, here and else- 
where, reveals himself as the calculator who kept Swift 
right in his proportions in the matter of the Lilliputians, 
Brobdingnagians, etc. Swift was very ignorant about things 
connected with number. He writes to Stella that he has 
discovered that leap-year comes every four years, and that 
all his life he had thought it came every three years. Did 
he begin with the mistake of Caesar's priests? Whether 
or no, when I find the person who did not understand leap- 
year inventing satellites of Mars in correct accordance with 
Kepler's third law, I feel sure he must have had help. 

THE AURORA BOREALIS. 

An essay concerning the late apparition in the heavens on the 
6th of March. Proving by mathematical, logical, and moral 
arguments, that it cou'd not have been produced meerly by the 
ordinary course of nature, but must of necessity be a prodigy. 
Humbly offered to the consideration of the Royal Society. Lon- 
don, 1716, 8vo. 

The prodigy, as described, was what we should call a 
very decided and unusual aurora borealis. The inference 
was, that men's sins were bringing on the end of the world. 
The author thinks that if one of the old "threatening 
prophets" were then alive, he would give "something like 
the following." I quote a few sentences of the notion 
which the author had of the way in which Ezekiel, for in- 
stance, would have addressed his Maker in the reign of 
George the First : 

"Begin! Begin! O Sovereign, for once, with an effec- 



THE AURORA BOREALIS. 135 

tual clap of thunder O Deity! either thunder to us no 

more, or when you thunder, do it home, and strike with 

vengeance to the mark Tis not enough to raise a storm, 

unless you follow it with a blow, and the thunder without 

the bolt, signifies just nothing at all Are then your 

lightnings of so short a sight, that they don't know how to 
hit, unless a mountain stands like a barrier in their way? 
Or perhaps so many eyes open in the firmament make you 
lose your aim when you shoot the arrow? Is it this? No! 
but, my dear Lord, it is your custom never to take hold 
of your arms till you have first bound round your majestic 
countenance with gathered mists and clouds." 

The principles of the Philosophy of the Expansive and Con- 
tractive Forces.... By Robert Greene, 1 M.A., Fellow of Clare 
Hall. Cambridge, 1727, folio. 

Sanderson 2 writes to Jones, 3 "The gentleman has been 
reputed mad for these two years last past, but never gave 
the world such ample testimony of it before." This was 
said of a former work of Greene's, on solid geometry, pub- 
lished in 1712, in which he gives a quadrature. 4 He gives 
the same or another, I do not know which, in the present 
work, in which the circle is 3% diameters. This volume is 
of 981 good folio pages, and treats of all things, mental and 
material. The author is not at all mad, only wrong on 

1 Greene (1678-1730) was a very eccentric individual and was 
generally ridiculed by his contemporaries. In his will he directed 
that his body be dissected and his skeleton hung in the library of 
King's College, Cambridge. Unfortunately for his fame, this wish 
was never carried out. 

2 This was the historian, Robert Sanderson (1660-1741), who 
spent most of his life at Cambridge. 

a l presume this was William Jones (1675-1749) the friend of 
Newton and Halley, vice-president of the Royal Society, in whose 
Synopsis Palmariorum Matheseos (1706) the symbol v is first used 
for the circle ratio. 

4 This was the Geometrica solidorum, sive materiae, seu de varia 
composition?, progressione, rationeque velo citatum, Cambridge, 1712. 
The work was parodied in A Taste of Philosophical Fanaticism. . .by 
a gentleman of the University of Gratz. 



136 A BUDGET OF PARADOXES. 

many points. It is the weakness of the orthodox follower 
of any received system to impute insanity to the solitary 
dissentient: which is voted (in due time) a very wrong 
opinion about Copernicus, Columbus, or Galileo, but quite 
right about Robert Greene. If misconceptions, acted on by 
too much self-opinion, be sufficient evidence of madness, it 
would be a curious inquiry what is the least per-centage 
of the reigning school which has been insane at any one 
time. Greene is one of the sources for Newton being led 
to think of gravitation by the fall of an apple : his authority 
is the gossip of Martin Folkes. 5 Probably Folkes had it 
from Newton's niece, Mrs. Conduitt, whom Voltaire ac- 
knowledges as his authority. 6 It is in the draft found among 
Conduitt's papers of memoranda to be sent to Fontenelle. 
But Fontenelle, though a great retailer of anecdote, does 
not mention it in his eloge of Newton ; whence it may be 
suspected that it was left out in the copy forwarded to 
France. D'Israeli has got an improvement on the story : 
the apple "struck him a smart blow on the head" : no doubt 
taking him just on the organ of causality. He was "sur- 
prised at the force of the stroke" from so small an apple: 
but then the apple had a mission ; Homer would have said 

8 The antiquary and scientist (1690-1754), president of the Royal 
Society, member of the Academic, friend of Newton, and authority 
on numismatics. 

6 She was Catherine Barton, Newton's step-niece. She marrie'd 
John Conduitt, master of the mint, who collected materials for a 
life of Newton. 

A propos of Mrs. Conduitt's life of her illustrious uncle, Sir 
George Greenhill tells a very good story on Poincare\ the well-known 
French mathematician. At an address given by the latter at the 
International Congress of Mathematicians held in Rome in 1908 he 
spoke of the story of Newton and the apple as a mere fable. After 
the address Sir George asked him why he had done so, saying that 
the story was first published by Voltaire,^ who had heard it from 
Newton s niece, Mrs. Conduitt. Poincare looked blank and said, 
"Newton, et la niece de Newton, et Voltaire, non ! je ne vous com- 
prends pas !" He had thought Sir George meant Professor Volterra 
of Rome, whose name in French is Voltaire, and who could not 
possibly have known a niece of Newton without bridging a century 
or so. 



THE AURORA BOREALIS. 137 

it was Minerva in the form of an apple. "This led him to 
consider the accelerating motion of falling bodies," which 
Galileo had settled long before: "from whence he deduced 
the principle of gravity," which many had considered be- 
fore him, but no one had deduced anything from it. I can- 
not imagine whence D'Israeli got the rap on the head, I 
mean got it for Newton: this is very unlike his usual ac- 
counts of things. The story is pleasant and possible: its 
only defect is that various writings, well known to Newton, 
a very learned mathematician, had given more suggestion 
than a whole sack of apples could have done, if they had 
tumbled on that mighty head all at once. And Pemberton, 
speaking from Newton himself, says nothing more than that 
the idea of the moon being retained by the same force which 
causes the fall of bodies struck him for the first time while 
meditating in a garden. One particular tree at Wools- 
thorpe has been selected as the gallows of the appleshaped 
goddess: it died in 1820, and Mr. Turner 7 kept the wood; 
but Sir D. Brewster 8 brought away a bit of root in 1814, 
and must have had it on his conscience for 43 years that 
he may have killed the tree. Kepler's suggestion of gravi- 
tation with the inverse distance, and Bouillaud's proposed 
substitution of the inverse square of the distance, are things 
which Newton knew better than his modern readers. I 
discovered two anagrams on his name, which are quite* con- 
clusive : the notion of gravitation was not new ; but Newton 
went on. Some wandering spirit, probably whose business 
it was to resent any liberty taken with Newton's name, put 
into the head of a friend of mine eighty-one anagrams on 
my own pair, some of which hit harder than any apple. 

7 This was the Edmund Turner (1755-1829) who wrote the Col- 
lections for the Town and Soke of Grantham, containing authentic 
Memoirs of Sir Isaac Newton, from Lord Portsmouth's Manuscripts, 
London, 1806. 

8 It may be recalled to mind that Sir David (1781-1868) wrote 
a life of Newton (1855). 



138 A BUDGET OF PARADOXES. 

DE MORGAN ANAGRAMS. 

This friend, whom I must not name, has since made it 
up to about 800 anagrams on my name, of which I have 
seen about 650. Two of them I have joined in the title- 
page: the reader may find the sense. A few of the others 
are personal remarks. 

"Great gun ! do us a sum !" 
is a sneer at my pursuits : but, 

"Go ! great sum ! fa* n du" 
is more dignified. 

"Sunt agro! gaudemus," 1 
is happy as applied to one of whom it may be said : 

"Ne'er out of town ; 'tis such a horrid life ; 
But duly sends his family and wife." 

"Adsum, nugator, suge!" 2 

is addressed to a student who continues talking after the 
lecture has commenced : oh ! the rascal ! 

"Graduatus sum ! nego" 3 

applies to one who declined to subscribe for an M.A. de- 
gree. 

"Usage mounts guard" 
symbolizes a person of very fixed habits. 

"Gus! Gus! a mature don! 

August man! sure, god! 
And Gus must argue, O ! 

Snug as mud to argue, 
Must argue on gauds. 

A mad rogue stung us. 
Gag a numerous stud. 

Go! turn us! damage us! 
Tug us ! O drag us ! Amen. 

Grudge us ! moan at us ! 

1 "They are in the country. We rejoice." 

2 "I am here, chatterbox, suck!" 

8 "I have been graduated ! I decline !" 



NEWTON'S DE MUNDI SYSTEMATE LIBER. 139 

Daunt us ! gag us more ! 

Dog-ear us, man! gut us! 
D us ! a rogue tugs !" 

are addressed to me by the circle-squarers ; and, 

"O ! Gus ! tug a mean surd!" 

is smart upon my preference of an incommensurable value 
of TT to 3%, or some such simple substitute. While, 

"Gus ! Gus ! at 'em a' round !" 

ought to be the backing of the scientific world to the author 
of the Budget of Paradoxes. 

The whole collection commenced existence in the head 
of a powerful mathematician during some sleepless nights. 
Seeing how large a number was practicable, he amused 
himself by inventing a digested plan of finding more. 

Is there any one whose name cannot be twisted into 
either praise or satire? I have had given to me, 

"Thomas Babington Macaulay 
Mouths big: a Cantab anomaly." 

NEWTON'S DE MUNDI SYSTEMATE LIBER. 

A treatise of the system -of the world. By Sir Isaac Newton. 
Translated into English. London, 1728, 8vo. 

I think I have a right to one little paradox of my own: 
I greatly doubt that Newton wrote this book. Castiglione, 1 
in his Newtoni Opuscula, 2 gives it in the Latin which ap- 
peared in 1731, 8 not for the first time; he says Angli omnes 
Newtono tribuunt. 4 It appeared just after Newton's death, 
without the name of any editor, or any allusion to Newton's 

^Giovanni Castiglioni (Castillon, Castiglione), was born at Cas- 
tiglione, in Tuscany, in 1708, and died at Berlin in 1791. He was 
professor of mathematics at Utrecht and at Berlin. He wrote on 
De Moivre's equations (1762), Cardan's rule (1783), and Euclid's 
treatment of parallels (1788-89). 

'This was the Isaaci Newtoni, equitis aurati, opuscula mathe- 
matica, philosophica et philologica, Lausannae & Genevae, 1744. 

"At London, 4to. 

"All the English attribute it to Newton.'" 



140 A BUDGET OF PARADOXES. 

recent departure, purporting to be that popular treatise 
which Newton, at the beginning of the third book of the 
Principia, says he wrote, intending it to be the third book. 
It is very possible that some observant turnpenny might 
construct such a treatise as this from the third book, that 
it might be ready for publication the moment Newton could 
not disown it. It has 'been treated with singular silence : 
the name of the editor has never been given. Rigaud 5 men- 
tions it without a word : I cannot find it in Brewster's New- 
ton, nor in the Biographia Britannica. There is no copy in 
the Catalogue of the Royal Society's Library, either in Eng- 
lish or Latin, except in Castiglione. I am open to correc- 
tion; but I think nothing from Newton's acknowledged 
works will prove as laid down in the suspected work 
that he took Numa's temple of Vesta, with a central fire, to 
be intended to symbolize the sun as the center of our sys- 
tem, in the Copernican sense. 6 

Mr. Edleston 7 gives an account of the lectures "de motu 
corporum," and gives the corresponding pages of the Latin 
"De Systemate Mundi" of 1731. But no one mentions the 
English of 1728. This English seems to agree with the 
Latin; but there is a mystery about it. The preface says, 
"That this work as here published is genuine will so clearly 
appear by the intrinsic marks it bears, that it will be but 
losing words and the reader's time to take pains in giving 
him any other satisfaction." Surely fewer words would 
have been lost if the prefator had said at once that the work 
was from the manuscript preserved at Cambridge. Perhaps 
it was a mangled copy clandestinely taken and interpreted. 

6 Stephen Peter Rigaud (1774-1839), Savilian professor of geom- 
etry at Oxford (1810-27) and later professor of astronomy and head 
of the Radcliffe Observatory. He wrote An historical Essay on the 
first publication of Sir Isaac Newton's Principia, Oxford, 1838, and 
a two-volume work entitled Correspondence of Scientific Men of the 
i^th Century, 1841. 

6 It is no longer considered by scholars as the work of Newton. 

7 J. Edleston, the author of the Correspondence of Sir Isaac 
Newton and Professor Cotes, London, 1850. 



A BACONIAN CONTROVERSY. 141 



A BACONIAN CONTROVERSY. 

Lord Bacon not the author of "The Christian Paradoxes," being 
a reprint of "Memorials of Godliness and Christianity," by 
Herbert Palmer, B.D. 1 With Introduction, Memoir, and Notes, 
by the Rev. Alexander B. Grosart, 2 Kenross. (Private circula- 
tion, 1864). 

I insert the above in this place on account of a slight 
connection with the last. Bacon's Paradoxes, so attributed 
were first published as his in some asserted "Remains," 
1648. 3 They were admitted into his works in 1730, and re- 
main there to this day. The title is "The Character of a 
believing Christian, set forth in paradoxes and seeming 
contradictions." The following is a specimen: 

"He believes three to be one and one to be three ; a father 
not to be older than his son; a son to be equal with his 
father; and one proceeding from both to be equal with 
both: he believes three persons in one nature, and two 
natures in one person. . . .He believes the God of all grace 
to have been angry with one that never offended Him ; and 
that God that hates sin to be reconciled to himself though 
sinning continually, and never making or being able to make 
Him any satisfaction. He believes a most just God to have 
punished a most just person, and to have justified himself, 
though a most ungodly sinner. He believes himself freely 
pardoned, and yet a sufficient satisfaction was made for 
him." 

Who can doubt that if Bacon had written this it must 
have been wrong? Many writers, especially on the Con- 

1 Palmer (1601-1647) was Master of Queen's College, Cam- 
bridge, a Puritan but not a separatist. His work, The Characters of 
a believing Christian, in Paradoxes and seeming contradictions, ap- 
peared in 1645. 

2 Grosart (1827-1899) was a Presbyterian clergyman. He was a 
great bibliophile, and issued numerous reprints of rare books. 

8 This was the year after Palmer's death. The title was, The 
Remaines of Francis Lord Verulam ; being Essays and sev- 
eral! Letters to severall great personages, and other pieces of various 
and high concernment not heretofore published, London, 1648, 4to. 



142 A BUDGET OF PARADOXES. 

tinent, have taken him as sneering at (Athanasian) Chris- 
tianity right and left. Many Englishmen have taken him 
to be quite in earnest, and to have produced a body of edi- 
fying doctrine. More than a century ago the Paradoxes were 
published as a penny tract; and, again, at the same price, 
in the Penny Sunday Reader, vol. vi, No. 148, a few pas- 
sages were omitted, as too strong. But all did not agree: 
in my copy of Peter Shaw's 4 edition (vol. ii, p. 283) the 
Paradoxes have been cut out by the binder, who has left 
the backs of the leaves. I never had the curiosity to see 
whether other copies of the edition have been served in the 
same way. The Religious Tract Society republished them 
recently in Selections from the Writings of Lord Bacon, (no 
date; bad plan; about 1863, I suppose). No omissions were 
made, so far as I find. 

I never believed that Bacon wrote this paper ; it has 
neither his sparkle nor his idiom. I stated my doubts even 
before I heard that Mr. Spedding, one of Bacon's editors, 
was of the same mind. (Athenceum, July 16, 1864). I was 
little moved by the wide consent of orthodox men: for I 
knew how Bacon, Milton, Newton, Locke, etc., were always 
claimed as orthodox until almost the present day. Of this 
there is a remarkable instance. 

LOCKE AND SOCINIANISM. 

Among the books which in my younger day were in 
some orthodox publication lists I think in the list of the 
Christian Knowledge Society, but I am not sure was 
Locke's 1 "Reasonableness of Christianity." It seems to have 
come down from the eighteenth century, when the battle 
was belief in Christ against unbelief, simpliciter, as the logi- 

4 Shaw (1694-1763) was physician extraordinary to George II. 
He wrote on chemistry and medicine, and his edition of the Philo- 
sophical Works of Francis Bacon appeared at London in 1733. 

1 John Locke (1632-1704), the philosopher. This particular work 
appeared in 1695. There was an edition in 1834 (vol. 25 of the 
Sacred Classics} and one in 1836 (vol. 2 of the Christian Library). 



LOCKE AND SOCINIANISM. 143 

cians say. Now, if ever there was a Socinian 2 book in the 
world, it is this work of Locke. ' These two," says Locke, 
"faith and repentance, i. e., believing Jesus to be the Mes- 
siah, and a good life, are the indispensable conditions of 
the new covenant, to be performed by all those who would 
obtain eternal life." All the book is amplification of this 
doctrine. Locke, in this and many other things, followed 
Hobbes, whose doctrine, in the Leviathan, is fidem, quanta 
ad salutem necessaria est, contineri in hoc articulo, Jesus 
est Christus. 3 For this Hobbes was called an atheist, which 

3 1 use the word Socinian because it was so much used in Locke's 
time; it is used in our own day by the small fry, the unlearned 
clergy and their immediate followers, as a term of reproach for all 
Unitarians. I suspect they have a kind of liking for the word; it 
sounds like so sinful. The learned clergy and the higher laity know 
better : they know that the bulk of the modern Unitarians go farther 
than Socinus, and are not correctly named as his followers. The 
Unitarians themselves neither desire nor deserve a name which puts 
them one point nearer to orthodoxy than they put themselves. That 
point is the doctrine that direct prayer to Jesus Christ is lawful and 
desirable : this Socinus held, and the modern Unitarians do not hold. 
Socinus, in treating the subject in his own Institutio, an imperfect cat- 
echism which he left, lays much more stress on John xiv. 13 than on xv. 
16 and xvi. 23 . He is not disinclined to think that Patrem should be 
in the first citation, where some put it; but he says that to ask the 
Father in the name of the Son is nothing but praying to the Son in 
prayer to the Father. He labors the point with obvious wish to secure 
a conclusive sanction. In the Racovian Catechism, of which Faustus 
Socinus probably drew the first sketch, a clearer light is arrived at. 
The translation says : "But wherein consists the divine honor due to 
Christ? In adoration likewise and invocation. For we ought at all 
times to adore Christ, and may in our necessities address our prayers 
to him as often as we please ; and there are many reasons to induce 
us to do this freely." There are some who like accuracy, even in 
aspersion. A. De M. 

Socinus, or Fausto Paolo Sozzini (1539-1604), was an anti- 
trinitarian who believed in prayer and homage to Christ. Leaving 
Italy after his views became known, he repaired to Basel, but his 
opinions were too extreme even for the ^ Calyinists. He then tried 
Transylvania, attempting to convert to his views the antitrinitarian 
Bishop David. The only result of his efforts was the imprisonment 
of David and his own flight to Poland, in which country he spent the 
rest of his life (1579-1604). His complete works appeared first at 
Amsterdam in 1668, in the Bibliotheca Fratres Polonorum. The Ra- 
covian Catechism (1605) appeared after his death, but it seems to 
have been planned by him. 

8 "As much of faith as is necessary to salvation is contained in 
this article, Jesus is the Christ." 



144 A BUDGET OF PARADOXES. 

many still believe him to have been: some of his contem- 
poraries called him, rightly, a Socinian. Locke was known 
for a Socinian as soon as his work appeared : Dr. John Ed- 
wards, 4 his assailant, says he is "Socinianized all over." 
Locke, in his reply, says "there is not one word of Socinian- 
ism in it:" and he was right: the positive Socinian doctrine 
has not one word of Socinianism in it ; Socinianism consists 
in omissions. Locke and Hobbes did not dare deny the 
Trinity: for such a thing Hobbes might have been roasted, 
and Locke might have been strangled. Accordingly, the 
well-known way of teaching Unitarian doctrine was the 
collection of the asserted essentials of Christianity, without 
naming the Trinity, etc. This is the plan Newton followed, 
in the papers which have at last been published. 5 

So I, for one, thought little about the general tendency 
of orthodox writers to claim Bacon by means of the Para- 
doxes. I knew that, in his "Confession of Faith" 8 he is a 
Trinitarian of a heterodox stamp. His second Person takes 
human nature before he took flesh, not for redemption, but 
as a condition precedent of creation. "God is so holy, pure, 
and jealous, that it is impossible for him to be pleased in 
any creature, though the work of his own hands. . . . [Gen. 
i. 10, 12, 18, 21, 25, 31, freely rendered]. But purposing 
to become a Creator, and to communicate to his creatures, 
he ordained in his eternal counsel that one person of the 
Godhead should be united to one nature, and to one par- 
ticular of his creatures ; that so, in the person of the Media- 
tor, the true ladder might be fixed, whereby God might 

'Edwards (1637-1716) was a Cambridge fellow, strongly Cal- 
vinistic. He published many theological works, attacking the Ar- 
minians and Socinians. Locke and Whiston were special objects of 
attack. 

*Sir I. Newton's views on points of Trinitarian Doctrine; his 
Articles of Faith, and the General Coincidence of his Opinions with 
those of J. Locke; a Selection of Authorities, with Observations, 
London, 1856. 

* A Confession of the Faith, Bristol, 1752, 8vo. 



LOCKE AND SOCINIANISM. 145 

descend to his creatures and his creatures might ascend to 
God...." 

This is republished by the Religious Tract Society, and 
seems to suit their theology, for they confess to having 
omitted some things of which they disapprove. 

In 1864, Mr. Grosart published his discovery that the 
Paradoxes are by Herbert Palmer ; that they were first pub- 
lished surreptitiously, and immediately afterwards by him- 
self, both in 1645; that the "Remains" of Bacon did not 
appear until 1648 ; that from 1645 to 1708, thirteen editions 
of the "Memorials" were published, all containing the Para- 
doxes. In spite of this, the Paradoxes were introduced 
into Bacon's works in 1730, where they have remained. 

Herbert Palmer was of good descent, and educated as 
a Puritan. He was an accomplished man, one of the few 
of his day who could speak French as well as English. He 
went into the Church, and was beneficed by Laud, 7 in spite 
of his puritanism; he sat in the Assembly of Divines, and 
was finally President of Queens' College, Cambridge, in 
which post he died, August 13, 1647, in the 46th year of 
his age. 

Mr. Grosart says, speaking of Bacon's "Remains," "All 
who have had occasion to examine our early literature are 
aware that it was a common trick to issue imperfect, false, 
and unauthorized writings under any recently deceased 
name that might be expected to take. The Puritans, down 
to John Bunyan, were perpetually expostulating and pro- 
testing against such procedure." I have met with instances 
of all this ; but I did not know that there was so much of 
it: a good collection would be very useful. The work of 
1728, attributed to Newton, is likely enough to be one of 
the class. 

T This was really very strange, because Laud (1573-1644), while 
he was Archbishop of Canterbury, forced a good deal of High 
Church ritual on the Puritan clergy, and even wished to compel the 
use of a prayer book in Scotland. It was this intolerance that led 
to his impeachment and execution. 



146 A BUDGET OF PARADOXES. 

Demonstration de I'immobiHtez de la Terre....Par M. de la 
Jonchere, 1 Ingenieur Francois. Londres, 1728, 8vo. 

A synopsis which is of a line of argument belonging 
to the beginning of the preceding century. 

TWO FORGOTTEN CIRCLE SQUARERS. 

The Circle squared; together with the Ellipsis and several re- 
flections on it. The finding two geometrical mean propor- 
tionals, or doubling the cube geometrically. By Richard Locke 1 
....London, no date, probably about 1730, 8vo. 

According to Mr. Locke, the circumference is three 
diameters, three-fourths the difference of the diameter and 
the side of the inscribed equilateral triangle, and three- 
fourths the difference between seven-eighths of the diameter 
and the side of the same triangle. This gives, he says, 
3. 18897. There is an addition to this tract, being an appen- 
dix to a book on the longitude. 

The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, 
Yorkshire. London, 1732, 8vo. 

Here 7r = 3.0625. No proof is offered. 2 

The longitude discovered by the Eclipses, Occultations, and 
Conjunctions of Jupiter's planets. By William Whiston. Lon- 
don, 1738. 

This tract has, in some copies, the celebrated preface 
containing the account of Newton's appearance before the 
Parliamentary Committee on the longitude question, in 1714 

"The name is Jonchere. He was a man of some merit^ pro- 
posing (1718) an important canal in Burgundy, and publishing a 
work on the Decouverte des longitudes estimees generalement im- 
possible a trouver, 1734 (or 1735). 

1 Locke invented a kind of an instrument for finding longitude, 
and it is described in the appendix, but I can find nothing about the 
man. There was published some years later (London, 1751) another 
work of his, A new Problem to discover the longitude at sea, 

* Baxter, concerning whom I know merely that he was a school- 
master, starts with the assumption of this value, and deduces from 
it some fourteen properties relating to the circle. 



THE STEAMSHIP SUGGESTED. 147 

(Brewster, ii. 257-266). This "historical preface," is an 
insertion and is dated April 28, 1741, with four additional 
pages dated August 10, 1741. The short "preface" is by the 
publisher, John Whiston,3 the author's son. 

THE STEAMSHIP SUGGESTED. 

A description and draught of a new-invented machine for carry- 
ing vessels or ships out of, or into any harbour, port, or river, 
against wind and tide, or in a calm. For which, His Majesty 
has granted letters patent, for the sole benefit of the author, 
for the space of fourteen years. By Jonathan Hulls. 1 London : 
printed for the author, 1737. Price sixpence (folding plate and 
pp. 48, beginning from title). 

(I ought to have entered this tract in its place. It is 
so rare that its existence was once doubted. It is the earliest 
description of steam-power applied to navigation. The 
plate shows a barge, with smoking funnel, and paddles at 
the stem, towing a ship of war. The engine, as described, 
is Newcomen's. 2 

In 1855, John Sheepshanks,^ so well known as a friend of 
Art and a public donor, reprinted this tract, in fac-simile, 
from his own copy ; twenty-seven copies of the original 
12mo size, and twelve on old paper, small 4to. I have an 
original copy, wanting the plate, and with "Price sixpence" 
carefully erased, to the honor of the book.* 

8 John, who died in 1780, was a well-known character in his way. 
He was a bookseller on Fleet Street, and his shop was a general 
rendezvous for the literary men of his time. He wrote the Memoirs 
of the Life and Writings of Mr. William Whiston (1749, with an- 
other edition in 1753). He was one of the first to issue regular 
catalogues of books with prices affixed. 

1 The name appears both as Hulls and as Hull. He was born in 
Gloucestershire in 1699. In 1754 he published The Art of Measuring 
made Easy by the help of a new Sliding Scale. 

"Thomas Newcomen (1663-1729) invented the first practical 
steam engine about 1710. It was of about five and a half horse 
power, and was used for pumping water from coal mines. Savery 
had described such an engine in 1702, but Newcomen improved upon 
it and made it practical. 

"The well-known benefactor of art (1787-1863). 

4 The tract was again reprinted in 1860. 



148 A BUDGET OF PARADOXES. 

It is not known whether Hulls actually constructed a 
boat. 5 In all probability his tract suggested to Symington, 
as Symington 6 did to Fulton.) 

THE NEWTONIANS ATTACKED. 

Le vrai systeme de physique generate de M. Isaac Newton ex- 
pose et analyse en parallele avec celui de Descartes. By Louis 
Castel 1 [Jesuit and F.R.S.] Paris, 1743, 4to. 

This is an elaborate correction of Newton's followers, 
and of Newton himself, who it seems did not give his own 
views with perfect fidelity. Father Castel, for instance, 
assures us that Newton placed the sun at rest in the center 
of the system. Newton left the sun to arrange that matter 
with the planets and the rest of the universe. In this vol- 
ume of 500 pages there is right and wrong, both clever. 

A dissertation on the yEther of Sir Isaac Newton. By Bryan 
Robinson, 2 M.D. Dublin, 1743, 8vo. 3 

8 Hulls made his experiment on the Avon, at Evesham, in 1737, 
having patented his machine in 1736. He had a Newcomen engine 
connected with six paddles. This was placed in the front of a small 
tow boat. The experiment was a failure. 

"William Symington (1763-1831). In 1786 he contructed a 
working model of a steam road carriage. The machinery was applied 
to a small boat in 1788, and with such success as to be tried on a 
larger boat in 1789. The machinery was clumsy, however, and in 
1801 he took out a new patent for the style of engine still used on 
paddle wheel steamers. This engine was successfully used in 1802, 
on the Charlotte Dundas. Fulton (1765-1815) was on board, and so 
impressed Robert Livingston with the idea that the latter furnished 
the money to build the Clermont (1807), the beginning of successful 
river navigation. 

1 Louis Bertrand Castel (1688-1757), most of whose life was 
spent in trying to perfect his Clavecin oculaire, an instrument on the 
order of the harpsichord, intended to produce melodies and har- 
monies of color. He also wrote L'Optique des couleurs (1740) and 
Sur le fond de la Musique (1754). 

8 Dr. Robinson (1680-1754) was professor of physic at Trinity 
College, Dublin, and three times president of King and Queen's 
College of Physicians. In his Treatise on the Animal Economy 
(1732-3, with a third edition in 1738) he anticipated the discoveries 
of Lavoisier and Priestley on the nature of oxygen. 

3 There was another edition, published at London in 1747, 8vo. 



MATHEMATICAL THEOLOGY. 149 

A mathematical work professing to prove that the as- 
sumed ether causes gravitation. 

MATHEMATICAL THEOLOGY. 

Mathematical principles of theology, or the existence of God 
geometrically demonstrated. By Richard Jack, teacher of 
Mathematics. London, 1747, Svo. 1 

Propositions arranged after the manner of Euclid, with 
beings represented by circles and squares. But these circles 
and squares are logical symbols, not geometrical ones. I 
brought this book forward to the Royal Commission on the 
British Museum as an instance of the absurdity of attempt- 
ing a classed catalogue from the titles of books. The title of 
this book sends it either to theology or geometry: when, 
in fact, it is a logical vagary. Some of the houses which 
Jack built were destroyed by the fortune of war in 1745, at 
Edinburgh: who will say the rebels did no good whatever? 
I suspect that Jack copied the ideas of J. B. Morinus, "Quod 
Deus sit," Paris, 1636, 2 4to, containing an attempt of the 
same kind, but not stultified with diagrams. 

TWO MODEL INDORSEMENTS. 

Dissertation, decouverte, et demonstrations de la quadrature 
mathematique du cercle. Par M. de Faure, geometre. [s. I, 
probably Geneva] 1747, Svo. 

Analyse de la Quadrature du Cercle. Par M. de Faure, Gentil- 
homme Suisse. Hague, I749, 1 4to. 

According to this octavo geometer and quarto gentle- 
man, a diameter of 81 gives a circumference of 256. There 
is an amusing circumstance about the quarto which has 
been overlooked, if indeed the book has ever been ex- 

*The author seems to have shot his only bolt in this work. I 
can find nothing about him. 

3 Quod Deus sit, mundusque ab ipso creatus fuerit in tempore, 
ejusque providentia gubernetur. Selecta aliquot theoremata adver- 
sos atheos, etc., Paris, 1635, 4to. 

*The British Museum Catalogue mentions a copy of 1740, but 
this is possibly a misprint. 



150 A BUDGET OF PARADOXES. 

amined. John Bernoulli (the one of the day) 2 and Koenig^ 
have both given an attestation: my mathematical readers 
may stare as they please, such is the fact. But, on examina- 
tion, there will be reason to think the two sly Swiss played 
their countryman the same trick as the medical man played 
Miss Pickle, in the novel of that name. The lady only 
wanted to get his authority against sousing her little nephew, 
and said, "Pray, doctor, is it not both dangerous and cruel 
to be the means of letting a poor tender infant perish by 
sousing it in water as cold as ice?" "Downright murder, 
I affirm," said the doctor; and certified accordingly. De 
Faure had built a tremendous scaffolding of equations, quite 
out of place, and feeling cock-sure that his solutions, if 
correct, would square the circle, applied to Bernoulli and 
Koenig who after his tract of two years before, must have 
known what he was at for their approbation of the solu- 
tions. And he got it, as follows, well guarded: 

"Suivant les suppositions posees dans ce Memoire, il est 
si evident que / doit etre = 34, y = 1, et z= 1, que cela n'a 
besoin ni de preuve ni d'autorite pour etre reconnu par tout 
le monde. 4 

"a Basle le 7e Mai 1749. JEAN BERNOULLI." 

"Je souscris au jugement de Mr. Bernoulli, en conse- 
quence de ces suppositions. 5 

"a la Haye le 21 Juin 1749. S. KOENIG." 

On which de Faure remarks with triumph as I have 
no doubt it was intended he should do "il conste clairement 
par ma presente Analyse et Demonstration, qu'ils y ont deja 

'This was Johann II (1710-1790), son of Johann I, who suc- 
ceeded his father as professor of mathematics at Basel. 

'Samuel Koenig (1712-1757), who studied under Johann Ber- 
noulli I. He became professor of mathematics at Franeker (1747) 
and professor of philosophy at the Hague (1749). 

4 "In accordance with the hypotheses laid down in this memoir it 
is so evident that / must =34, y = I, and = i, that there is no 
need of proof or authority for it to be recognized by every one." 

B "I subscribe to the judgment of Mr. Bernoulli as a result of 
these hypotheses." 



THOMAS WRIGHT OF DURHAM. 151 

reconnu et approuve parfaitement que la quadrature du 
cercle est mathematiquement demontree." 6 It should seem 
that it is easier to square the circle than to get round a 
mathematician. 

An attempt to demonstrate that all the Phenomena in Nature 
may be explained by two simple active principles, Attraction 
and Repulsion, wherein the attraction of Cohesion, Gravity 
and Magnetism are shown to be one and the same. By Gowin 
Knight. London, 1748, 4to. 

Dr. Knight 7 was Mr. Panizzi's 8 archetype, the first Prin- 
cipal Librarian of the British Museum. He was celebrated 
for his magnetical experiments. This work was long neg- 
lected ; but is now recognized as of remarkable resemblance 
to modern speculations. 

THOMAS WRIGHT OF DURHAM. 

An original theory or Hypothesis of the Universe. By Thomas 
Wright 1 of Durham. London, 4to, 1750. 

Wright is a speculator whose thoughts are now part of 
our current astronomy. He took that view or most of it 
of the milky way which afterwards suggested itself to Wil- 
liam Herschel. I have given an account of him and his 
work in the Philosophical Magazine for April, 1848. 

Wright was mathematical instrument maker to the King ; 

8 "It clearly appears from my present analysis and demonstration 
that they have already recognized and perfectly agreed to the fact 
that the quadrature of the circle is mathematically demonstrated." 

T Dr. Knight (died in 1772) made some worthy contributions to 
the literature of the mariner's compass. As De Morgan states, he 
was librarian of the British Museum. 

8 Sir Anthony Panizzi (1797-1879) fled from Italy under sen- 
tence of death (1822). He became assistant (1831) and chief 
(1856) librarian of the British Museum, and was knighted in 1869. 
He began the catalogue of printed books of the Museum. 

1 Wright (1711-1786) was a physicist. He was offered the pro- 
fessorship of mathematics at the Imperial Academy of St. Peters- 
burg but declined to accept it. This work is devoted chiefly to the 
theory of the Milky Way, the via lactea as he calls it after the man- 
ner of the older writers. 



152 A BUDGET OF PARADOXES. 

and kept a shop in Fleet Street. Is the celebrated business 
of Troughton & Simms, also in Fleet Street, a lineal des- 
cendant of that of Wright ? It is likely enough, more likely 
that that as I find him reported to have affirmed Prester 
John was the descendant of Solomon and the Queen of 
Sheba. Having settled it thus, it struck me that I might 
apply to Mr. Simms, and he informs me that it is as I 
thought, the line of descent being Wright, Cole, John 
Troughton, Edward Troughton, 2 Troughton & Simms.s 

BISHOP HORNE ON NEWTON. 

The theology and philosophy in Cicero's Somnium Scipionis 
explained. Or, a brief attempt to demonstrate, that the New- 
tonian system is perfectly agreeable to the notions of the 
wisest ancients : and that mathematical principles are the only 
sure ones. [By Bishop Home, 1 at the age of nineteen.] Lon- 
don, 1751, 8vo. 

This tract, which was not printed in the collected works, 
and is now excessively rare, is mentioned in Notes and Que- 
ries, 1st S., v, 490, 573; 2d S., ix, 15. The boyish satire 
on Newton is amusing. Speaking of old Benjamin Martin, 2 
he goes on as follows: 

2 Troughton (1753-1835) was one of the world's greatest in- 
strument makers. He was apprenticed to his brother John, and the 
two succeeded (1770) Wright and Cole in Fleet Street. Airy called 
his method of graduating circles the greatest improvement ever 
made in instrument making. He constructed (1800) the first modern 
transit circle, and his instruments were used in many of the chief 
observatories of the world. 

'William Simms (1793-1860) was taken into partnership by 
Troughton (1826) after the death of the latter's brother. The firm 
manufactured some well-known instruments. 

J This was George Home (1730-1792), fellow of Magdalen Col- 
lege, Oxford, vice-Chancellor of the University (1776), Dean of 
Canterbury (1781), and Bishop of Norwich (1790). He was a great 
satirist, but most of his pamphlets against men like Adam Smith, 
Swedenborg, and Hume, were anonymous, as in the case of this 
one against Newton. He was so liberal in his attitude towards the 
Methodists that he would not have John Wesley forbidden to preach 
in his diocese. He was twenty-one when this tract appeared. 

a Martin (1704-1782) was by no means "old Benjamin Martin" 
when Home wrote this pamphlet in 1749. In fact he was then only 



BISHOP HORNE ON NEWTON. 153 

"But the most elegant account of the matter [attraction] 
is by that hominiform animal, Mr. Benjamin Martin, who 
having attended Dr. Desaguliers'3 fine, raree, gallanty shew 
for some years [Desaguliers was one of the first who gave 
public experimental lectures, before the saucy boy was born] 
in the capacity of a turnspit, has, it seems, taken it into his 
head to set up for a philosopher." 

Thus is preserved the fact, unknown to his biographers, 
that Benj. Martin was an assistant to Desaguliers in his 
lectures. Hutton* says of him, that "he was well skilled in the 
whole circle of the mathematical and philosophical sciences, 
and wrote useful books on every one of them" : this is quite 
true ; and even at this day he is read by twenty where Home 
is read by one ; see the stalls, passim. All that I say of him, in- 
deed my knowledge of the tract, is due to this contemptuous 
mention of a more durable man than himself. My assistant 
secretary at the Astronomical Society, the late Mr. Epps,s 
bought the copy at a stall because his eye was caught by the 
notice of "Old Ben Martin," of whom he was a great reader. 
Old Ben could not be a Fellow of the Royal Society, because he 
kept a shop: even though the shop sold nothing but philo- 
sophical instruments. Thomas Wright, similarly situated 
as to shop and goods, never was a Fellow. The Society 
of our day has greatly degenerated : those of the old time 
would be pleased, no doubt, that the glories of their day 

forty-five. He was a physicist and a well-known writer on scientific 
instruments. He also wrote Philosophic, Britannica or a new and 
comprehensive system of the Newtonian Philosophy (1759). 

3 Jean Theophile Desaguliers, or Des Aguliers (1683-1744) was 
the son of a Protestant who left France after the revocation of the 
Edict of Nantes. He became professor of physics at Oxford, and 
afterwards gave lectures in London. Later he became chaplain to 
the Prince of Wales. He published several works on physics. 

4 Charles Hutton (1737-1823), professor of mathematics at Wool- 
wich (1772-1807). His Mathematical Tables (1785) and Mathemat- 
ical and Philosophical Dictionary (1795-1796) are well known. 

5 James Epps (1773-1839) contributed a number of memoirs on 
the use and corrections of instruments. He was assistant secretary 
of the Astronomical Society. 



154 A BUDGET OF PARADOXES. 

should be commemorated. In the early days of the Society, 
there was a similar difficulty about Graunt, the author of 
the celebrated work on mortality. But their royal patron, 
"who never said a foolish thing," sent them a sharp mes- 
sage, and charged them if they found any more such trades- 
men, they should "elect them without more ado." 

Home's first pamphlet was published when he was but 
twenty-one years old. Two years afterwards, being then 
a Fellow of his college, and having seen more of the world, 
he seems to have felt that his manner was a little too pert. 
He endeavored, it is said, to suppress his first tract: and 
copies are certainly of extreme rarity. He published the 
following as his maturer view: 

A fair, candid, and impartial state of the case between Sir 
Isaac Newton and Mr. Hutchinson. 6 In which is shown how 
far a system of physics is capable of mathematical demonstra- 
tion ; how far Sir Isaac's, as such a system, has that demon- 
stration; and consequently, what regard Mr. Hutchinson' s 
claim may deserve to have paid to it. By George Home, M.A. 
Oxford, 1753, 8vo. 

It must be remembered that the successors of Newton 
were very apt to declare that Newton had demonstrated 
attraction as a physical cause : he had taken reasonable pains 
to show that he did not pretend to this. If any one had 
said to Newton, I hold that every particle of matter is a 
responsible being of vast intellect, ordered by the Creator 
to move as it would do if every other particle attracted it, 
and gifted with- power to make its way in true accordance 
with that law, as easily as a lady picks her way across the 
street ; what have you to say against it ? Newton must 
have replied, Sir! if you really undertake to maintain this 
as demonstrable, your soul had better borrow a little power 

'John Hutchinson (1674-1737) was one of the first to ^ try to 
reconcile the new science of geology with Genesis. He denied the 
Newtonian hypothesis as dangerous to religion, and because it ne- 
cessitated a vacuum. He was a mystic in his interpretation of the 
Scriptures, and created a sect that went under the name of Hutchin- 
sonians. 



BISHOP HORNE ON NEWTON. 155 

from the particles of which your body is made: if you 
merely ask me to refute it, I tell you that I neither can nor 
need do it ; for whether attraction comes in this way or in 
any other, it comes, and that is all I have to do with it. 

The reader should remember that the word attraction, 
as used by Newton and the best of his followers, only meant 
a drawing towards, without any implication as to the cause. 
Thus whether they said that matter attracts .matter, or that 
young lady attracts young gentleman, they were using one 
word in one sense. Newton found that the law of the first 
is the inverse square of the distance: I am not aware that 
the law of the second has been discovered ; if there be any 
chance, we shall see it at the year 1856 in this list. 

In this point young Home made a hit. He justly cen- 
sures those who fixed upon Newton a more positive knowl- 
edge of what attraction is than he pretended to have. "He 
has owned over and over he did not know what he meant 
by it it might be this, or it might be that, or it might be 
anything, or it might be nothing." With the exception of 
the nothing clause, this is true, though Newton might have 
answered Home by "Thou hast said it." 

(I thought everybody knew the meaning of "Thou hast 
said it": but I was mistaken. In three of the evangelists 
2v Aeyeis is the answer to "Art thou a king?" The force of 
this answer, as always understood, is "That is your way 
of putting it." The Puritans, who lived in Bible phrases, 
so understood it : and Walter Scott, who caught all peculiar- 
ities of language with great effect, makes a marked instance, 
"Were you armed? I was not I went in my calling, as 
a preacher of God's word, to encourage them that drew 
the sword in His cause. In other words, to aid and abet 
the rebels, said the Duke. Thou hast spoken it, replied the 
prisoner.") 

Again, Home quotes Rowning 7 as follows: 

7 John Rowning, a Lincolnshire rector, died in 1771. He wrote on 



156 A BUDGET OF PARADOXES. 

"Mr. Rowning, pt. 2, p. 5 in a note, has a very pretty 
conceit upon this same subject of attraction, about every 
particle of a fluid being intrenched in three spheres of 
attraction and repulsion, one within another, 'the innermost 
of which (he says) is a sphere of repulsion, which keeps 
them from approaching into contact; the next, a sphere of 
attraction, diffused around this of repulsion, by which the 
particles are disposed to run together into drops; and the 
outermost of all, a sphere of repulsion, whereby they repel 
each other, when removed out of the attraction.' So that 
between the urglngs, and solicitations, of one and t'other, 
a poor unhappy particle must ever be at his wit's end, not 
knowing which way to turn, or whom to obey first." 

Rowning has here started the notion which Boscovich 8 
afterwards developed. 

I may add to what precedes that it cannot be settled that, 
as Grange^ says, Desaguliers was the first who gave ex- 
perimental lectures in London. William Whiston gave some, 
and Francis Hauksbee 10 made the experiments. The prospec- 
tus, as we should now call it, is extant, a quarto tract of 
plates and descriptions, without date. Whiston, in his life, 

physics, and published a memoir on A machine for finding the roots 
of equations universally (1770). 

8 It is always difficult to sanction this spelling of the name of this 
Jesuit father who is so often mentioned in the analytic treatment of 
conies. He was born in Ragusa in 1711, and the original spelling was 
RuSer Josip Boskovic. When he went to live in Italy, as professor 
of mathematics at Rome (1740) and at Pavia, the name was spelled 
Ruggiero Giuseppe Boscovich, although Boscovicci would seem to 
a foreigner more natural. His astronomical work was notable, and 
in his De maculis solaribus (1736) there is the first determination 
of the equator of a planet by observing the motion of spots on its 
surface. Boscovich came near having some contact with America, 
for he was delegated to observe in California the transit of Venus 
in 1755, being prevented by the dissolution of his order just at that 
time. He died in 1787, at Milan. 

* James Granger (1723-1776) who wrote the Biographical His- 
tory of England, London, 1769. His collection of prints was re- 
markable, numbering some fourteen thousand. 

10 He was curator of experiments for the Royal Society. He 
wrote a large number of books and monographs on physics. He 
died about 1713. 



FALLACIES IN A THEORY OF ANNUITIES. 157 

gives 1714 as the first date of publication, and therefore, 
no doubt, of the lectures. Desaguliers removed to London 
soon after 1712, and commenced his lectures soon after that. 
It will be rather a nice point to settle which lectured first; 
probabilities seem to go in favor of Whiston. 

FALLACIES IN A THEORY OF ANNUITIES. 

An Essay to ascertain the value of leases, and annuities for 
years and lives. By W[eyman] L[ee]. London, 1737, 8vo. 

A valuation of Annuities and Leases certain, for a single life. 
By Weyman Lee, Esq. of the Inner Temple. London, 1751, 
8vo. Third edition, 1773. 

. Every branch of exact science has its paradoxer. The 
world at large cannot tell with certainty who is right in 
such questions as squaring the circle, etc. Mr. Weyman 
Lee 1 was the assailant of what all who had studied called 
demonstration in the question of annuities. He can be ex- 
posed to the world : for his error arose out of his not being 
able to see that the whole is the sum of all its parts. 

By an annuity, say of 100, now bought, is meant that 
the buyer is to have for his money 100 in a year, if he be 
then alive, 100 at the end of two years, if then alive, and so 
on. It is clear that he would buy a life annuity if he should 
buy the first 100 in one office, the second in another, and 
so on. All the difference between buying the whole from 
one office and buying all the separate contingent payments 
at different offices, is immaterial to calculation. Mr. Lee 
would have agreed with the rest of the world about the 
payments to be made to the several different offices, in con- 
sideration of their several contracts: but he differed from 
every one else about the sum to be paid to one office. He 
contended that the way to value an annuity is to find out 
the term of years which the individual has an even chance 
of surviving, and to charge for the life annuity the value of 
an annuity certain for that term. 

1 Lee seems to have made no impression on biographers. 



158 A BUDGET OF PARADOXES. 

It is very common to say that Lee took the average life, 
or expectation, as it is wrongly called, for his term: and 
this I have done myself, taking the common story. Having 
exposed the absurdity of this second supposition, taking it 
for Lee's, in my Formal Logic, 2 I will now do the same with 
the first. 

A mathematical truth is true in its extreme cases. Lee's 
principle is that an annuity on a life is the annuity made 
certain for the term within which it is an even chance the 
life drops. If, then, of a thousand persons, 500 be sure to 
die within a year, and the other 500 be immortal, Lee's 
price of an annuity to any one of these persons is the 
present value of one payment: for one year is the term 
which each one has an even chance of surviving and not 
surviving. But the true value is obviously half that of a 
perpetual annuity: so that at 5 percent Lee's rule would 
give less than the tenth of the true value. It must be said 
for the poor circle-squarers, that they never err so much 
as this. 

Lee would have said, if alive, that I have put an extreme 
case: but any universal truth is true in its extreme cases. 
It is not fair to bring forward an extreme case against a 
person who is speaking as of usual occurrences: but it is 
quite fair when, as frequently happens, the proposer insists 
upon a perfectly general acceptance of his assertion. And 
yet many who go the whole hog protest against being tickled 
with the tail. Counsel in court are good instances : they are 
paradoxers by trade. June 13, 1849, at Hertford, there was 
an action about a ship, insured against a total loss: some 
planks were saved, and the underwriters refused to pay. 
Mr. Z. (for deft.) "There can be no degrees of totality; and 
some timbers were saved." L. C. B. "Then if the vessel 
were burned to the water's edge, and some rope saved in 
the boat, there would be no total loss." Mr. Z. "This is 
putting a very extreme case." L. C. B. "The argument 

2 This work appeared at London in 1852. 



MONTUCLA'S WORK ON THE QUADRATURE. 159 

would go that length." What would Judge Z. as he now 
is say to the extreme case beginning somewhere between 
six planks and a bit of rope? 

MONTUCLA'S WORK ON THE QUADRATURE. 
Histoire des recherches sur la quadrature du cercle. . . .avec 
une addition concernant les problemes de la duplication du 
cube et de la trisection de Tangle. Paris, 1754, I2mo. [By 
Montucla.] 

This is the history of the subject. 1 It was a little episode 
to the great history of mathematics by Montucla, of which 
the first edition appeared in 1758. There was much addition 
at the end of the fourth volume of the second edition ; this 
is clearly by Montucla, though the bulk of the volume is put to- 
gether, with help from Montucla's papers, by Lalande. 2 There 
is also a second edition of the history of the quadrature, 
Paris, 1831, 8vo, edited, I think, by Lacroix; of which it 
is the great fault that it makes hardly any use of the addi- 
tional matter just mentioned. 

Montucla is an admirable historian when he is writing 
from his own direct knowledge : it is a sad pity that he did 
not tell us when he was depending on others. We are not 
to trust a quarter of his book, and we must read many 
other books to know which quarter. The fault is common 
enough, but Montucla's good three-quarters is so good that 
the fault is greater in him than in most others: I mean the 
fault of not acknowledging; for an historian cannot read 
everything. But it must be said that mankind give little 
encouragement to candor on this point. Hallam, in his 

1 Of course this is no longer true. The most scholarly work 
to-day is that of Rudio, Archimedes, Huygens, Lambert, Legendre, 
vier Abhandlungen uber die Kreismessung. . . .mit einer Uebersicht 
iibcr die Geschichte des Problems von der Quadratur des Zirkels, 
von den 'dltesten Zeiten bis auf unsere Tage, Leipsic, 1892. 

2 Joseph Jerome le Francois de Lalande (1732-1807), professor 
of astronomy in the College de France (1753) and director of the 
Paris Observatory (1761). His writings on astronomy and his Bib- 
liographic astronomique, avec I'histoire de I'astronomie depuis 1781 
jusqu'en 1802 (Paris, 1803) are well known. 



160 A BUDGET OF PARADOXES. 

History of Literature, states with his own usual instinct 
of honesty every case in which he depends upon others : 
Montucla does not. And what is the consequence? Mon- 
tucla is trusted, and believed in, and cried up in the bulk ; 
while the smallest talker can lament that Hallam should 
be so unequal and apt to depend on others, without remem- 
bering to mention that Hallam himself gives the informa- 
tion. As to a universal history of any great subject being 
written entirely upon primary knowledge, it is a thing of 
which the possibility is not yet proved by an example. De- 
lambre attempted it with astronomy, and was removed by 
death before it was finished,3 to say nothing of the gaps 
he left. 

Montucla was nothing of a bibliographer, and his de- 
scriptions of books in the first edition were insufficient. The 
Abbe Rive 4 fell foul of him, and as the phrase is, gave it 
him. Montucla took it with great good humor, tried to 
mend, and, in his second edition, wished his critic had lived 
to see the vernis de bibliographe which he had given himself. 

I have seen Montucla set down as an esprit fort, more 
than once: wrongly, I think. When he mentions Barrow'ss 
address to the Almighty, he adds, "On voit, au reste, par la, 
que Barrow etoit un pauvre philosophe; car il croyait en 
rimmortalite de Tame, et en une Divinite autre que la nature 



8 De Morgan refers to his Histoire de I' Astronomic au i8e siccle, 
which appeared in 1827, five years after Delambre's death. Jean 
Baptiste Joseph Delambre (1749-1822) was a pupil of and a collabo- 
rator with Lalande, following his master as professor of astronomy 
in the College de France. His work on the measurements for the 
metric system is well known, and his four histories of astronomy, 
ancienne (1817), au moyen age (1819), moderne (1821), and au i8e 
siecle (posthumous, 1827) are highly esteemed. 

4 Jean- Joseph Rive (1730-1792), a priest who left his cure under 
grave charges, and a quarrelsome character. His attack on Mon- 
tucla was a case of the pot calling the kettle black ; for while he was 
a brilliant writer he was a careless bibliographer. 

5 Isaac Barrow (1630-1677) was quite as well known as a theo- 
logian as he was from his Lucasian professorship of mathematics at 
Cambridge. 



MONTUCLA'S WORK ON THE QUADRATURE. 161 

universelle." This is irony, not an expression of opinion. 
In the book of mathematical recreations which Montucla 
constructed upon that of Ozanam, 7 and Ozanam upon that 
of Van Etten, 8 now best known in England by Hutton's 
similar treatment of Montucla, there is an amusing chapter 
on the quadrators. Montucla refers to his own anonymous 
book of 1754 as a curious book published by Jombert. 9 He 
seems to have been a little ashamed of writing about circle- 
squarers : what a slap on the face for an unborn Budgeteer ! 
Montucla says, speaking of France, that he finds three 
notions prevalent among the cyclometers: (1) that there 
is a large reward offered for success; (2) that the longitude 
problem depends on that success; (3) that the solution is 
the great end and object of geometry. The same three 

8 "Besides we can see by this that Barrow was a poor philosopher ; 
for he believed in the immortality of the soul and in a Divinity 
other than universal nature." 

T The Recreations mathematiques et physiques (Paris, 1694) of 
Jacques Ozanam (1640-1717) is a work that is still highly esteemed. 
Among various other works he wrote a Dictionnaire mathematique 
ou Idee generate des mathematiques (1690) that was not without 
merit. The Recreations went through numerous editions (Paris, 
1694, 1696, 1741, 1750, 1770, 1778, and the Montucla edition of 1790; 
London, 1708, the Montucla-Hutton edition of 1803 and the Riddle 
edition of 1840; Dublin, 1790). 

8 Hendryk van Etten, the nom de plume of Jean Leurechon 
(1591-1670), rector of the Jesuit college at Bar, and professor of 
philosophy and mathematics. He wrote on astronomy (1619) and 
horology (1616), and is known for his Selecta Propositipnes in tota 
sparsim mathematica pulcherrime propositae in solemni festo SS. 
Ignatii et Francesci Xaverii, 1622. The book to which De Morgan 
refers is his Recreation mathematicque, composee de plusieurs pro- 
blcmes plaisants et facetieux, Lyons, 1627, with an edition at Pont- 
a-Mousson, 1629. There were English editions published at London 
in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672. 

I do not understand how De Morgan happened to miss own- 
ing the work by Claude Caspar Bachet de Meziriac (1581-1638), 
Problcmes plaisans et detectable*, which appeared at Lyons in 1612, 
8vo, with a second edition in 1624. There was a fifth edition pub- 
lished at Paris in 1884. 

9 His title page closes with "Paris, Chez Ch. Ant. Jombert 

M.DCC.LIV." 

This was Charles- Antoine Jombert (1712-1784), a printer and 
bookseller with some taste for painting and architecture. He wrote 
several works and edited a number of early treatises. 



162 A BUDGET OF PARADOXES.- 

notions are equally prevalent among the same class in Eng- 
land. No reward has ever been offered by the government 
of either country. The longitude problem in no way de- 
pends upon perfect solution; existing approximations are 
sufficient to a point of accuracy far beyond what can be 
wanted. 10 And geometry, content with what exists, has long 
passed on to other matters. Sometimes a cyclometer per- 
suades a skipper who has made land in the wrong place 
that the astronomers are in fault, for using a wrong measure 
of the circle; and the skipper thinks it a very comfortable 
solution ! And this is the utmost that the problem ever has 
to do with longitude. 

ANTINEWTONIANISMUS. 

Antinewtonianismus. 1 By Caelestino Cominale, 2 M.D. Naples, 
1754 and 1756, 2 vols. 4to. 

The first volume upsets the theory of light; the second 
vacuum, vis inertise, gravitation, and attraction. I confess 
I never attempted these big Latin volumes, numbering 450 
closely-printed quarto pages. The man who slays Newton 
in a pamphlet is the man for me. But I will lend them to 
anybody who will give security, himself in 500, and two 
sureties in 250 each, that he will read them through, and 
give a full abstract; and I will not exact security for their 
return. I have never seen any mention of this book : it has 
a printer, but not a publisher, as happens with so many un- 
recorded books. 

10 The late Professor Newcomb made the matter plain even to 
the non-mathematical mind, when he said that "ten decimal places 
are sufficient to give the circumference of the earth to the fraction 
of an inch, and thirty decimal places would give the circumference 
of the whole visible universe to a quantity imperceptible with the 
most powerful microscope." 

1 Antinewtonianismi pars prima, in qua Newtoni de coloribus 
systema ex propriis principiis geometrice evertitur, et nova de colori- 
bus theoria luculentissimis experiments demonstrantur . .. .Naples, 
1 754'> pars secunda, Naples, 1756. 

2 Celestino Cominale (1722-1785) was professor of medicine at 
the University of Naples. 



OFFICIAL BLOW TO CIRCLE SQUARERS. 163 



OFFICIAL BLOW TO CIRCLE SQUARERS. 

1755. The French Academy of Sciences came to the 
determination not to examine any more quadratures or 
kindred problems. This was the consequence, no doubt, 
of the publication of Montucla's book: the time was well 
chosen ; for that book was a full justification of the resolu- 
tion. The Royal Society followed the same course, I be- 
lieve, a few years afterwards. When our Board of Longi- 
tude was in existence, most of its time was consumed in 
listening to schemes, many of which included the quadrature 
of the circle. It is certain that many quadrators have im- 
agined the longitude problem to be connected with theirs: 
and no doubt the notion of a reward offered by Government 
for a true quadrature is a result of the reward offered for 
the longitude. Let it also be noted that this longitude re- 
ward was not a premium upon excogitation of a mysterious 
difficulty. The legislature was made to know that the 
rational hopes of the problem were centered in the improve- 
ment of the lunar tables and the improvement of chronom- 
eters. To these objects alone, and by name, the offer was 
directed: several persons gained rewards for both; and the 
offer was finally repealed. 

AN INTERESTING HOAX. 

Fundamentalis Figura Geometrica, primas tantum lineas circuli 
quadrature possibilitatis ostendens. By Niels Erichsen (Nico- 
laus Ericius), shipbuilder, of Copenhagen. Copenhagen, 1755, 
I2mo. 

This was a gift from my oldest friend who was not a 
relative, Dr. Samuel Maitland of the "Dark Ages." 1 He 
found it among his books, and could not imagine how he 
came by it: I could have told him. He once collected 
interpretations of the Apocalypse: and auction lots of such 

1 The work appeared in the years from 1844 to 1849. 



164 A BUDGET OF PARADOXES. 

books often contain quadratures. The wonder is he never 
found more than one. 

The quadrature is not worth notice. Erichsen is the only 
squarer I have met with who has distinctly asserted the par- 
ticulars of that reward which has been so frequently thought 
to have been offered in England. He says that in 1747 the 
Royal Society on the 2d of June, offered to give a large re- 
ward for the quadrature of the circle and a true explanation 
of magnetism, in addition to 30,000 previously promised for 
the same. I need hardly say that the Royal Society had 
not 30,000 at that time, and would not, if it had had such 
a sum, have spent it on the circle, nor on magnetic theory; 
nor would it have coupled the two things. On this book, 
see Notes and Queries, 1st S., xii, 306. Perhaps Erichsen 
meant that the 30,000 had been promised by the Govern- 
ment, and the addition by the Royal Society. 

October 8, 1866. I receive a letter from a cyclometer 
who understands that a reward is offered to any one who 
will square the circle, and that all competitors are to send 
their plans to me. The hoaxers have not yet failed out of 
the land. 

TWO JESUIT CONTRIBUTIONS. 

Theoria Philosophise Naturalis redacta ad unicam legem virium 
in natura existentium. Editio Veneta prima. By Roger Joseph 
Boscovich. Venice, 1763, 4to. 

The first edition is said to be of Vienna, 1758. 1 This 
is a celebrated work on the molecular theory of matter, 
grounded on the hypothesis of spheres of alternate attrac- 
tion and repulsion. Boscovich was a Jesuit of varied pur- 
suit. During his measurement of a degree of the meridian, 
while on horseback or waiting for his observations, he com- 
posed a Latin poem of about five thousand verses on eclipses, 

1 There was a Vienna edition in 1758, 4to, and another in 1759, 
4to. This edition is described on the title page as Editio Veneta 
prima ipso auctore praesente, et corrigente. 



TWO JESUIT CONTRIBUTIONS. 165 

[with notes, which he dedicated to the Royal Society: De 
\Solis et LuncE defectibus, 2 London, Millar and Dodsley, 
1760, 4to. 

Traite de paix entre Des Cartes et Newton, precede des vies 
litteraires de ces deux chefs de la physique moderne. . .By Aime 
Henri Paulian. 3 Avignon, 1763, I2mo. 

I have had these books for many years without feeling 
the least desire to see how a lettered Jesuit would atone 
Descartes and Newton. On looking at my two volumes, I 
find that one contains nothing but the literary life of Des- 
cartes; the other nothing but the literary life of New- 
ton. The preface indicates more: and Watt mentions three 
volumes. 4 I dare say the first two contain all that is valu- 
able. On looking more attentively at the two volumes, I 
find them both readable and instructive; the account of 
Newton is far above that of Voltaire, but not so popular. 
But he should not have said that Newton's family came from 
Newton in Ireland. Sir Rowland Hill gives fourteen New- 
tons in Ireland :S twice the number of the cities that con- 
tended for the birth of Homer may now contend for the 
origin of Newton, on the word of Father Paulian. 

Philosophical Essays, in three parts. By R. Lovett, Lay Clerk 

of the Cathedral Church of Worcester. Worcester, 1766, 8vo. 

The Electrical Philosopher: containing a new system of physics 

8 The first edition was entitled De solis ac lunae defectibus libri 
V. P. Rogerii Jose phi Boscovich. . . . cum ejusdem auctoris adnota- 
tionibus, London, 1760. It also appeared in Venice in 1761, and in 
French translation by the Abbe de Baruel in 1779, and was a work 
of considerable influence. 

Paulian (1722-1802) was professor of physics at the Jesuit 
college at Avignon. He wrote several works, the most popular of 
which, the Dictionnaire de physique (Avignon, 1761), went through 
nine editions by 1789. 

4 This is correct. 

5 Probably referring to the fact that Hill (1795-1879), who had 
done so much for postal reform, was secretary to the postmaster 
general (1846), and his name was a synonym for the post office 
directory. 



166 A BUDGET OF PARADOXES. 

founded upon the principle of an universal Plenum of ele- 
mentary fire By R. Lovett, Worcester, 1774, 8vo. 

Mr. Lovett 6 was one of those ether philosophers who 
bring in elastic fluid as an explanation by imposition of 
words, without deducing any one phenomenon from what 
we know of it. And yet he says that attraction has received 
no support from geometry; though geometry, applied to 
a particular law of attraction, had shown how to predict the 
motions of the bodies of the solar system. He, and many 
of his stamp, have not the least idea of the confirmation 
of a theory by accordance of deduced results with observa- 
tion posterior to the theory. 

BAILLY'S EXAGGERATED VIEW OF ASTRONOMY. 

Lettres sur 1'Atlantide de Platon, et sur 1'ancien Histoire de 
1'Asie, pour servir de suite aux lettres sur 1'origine des Sci- 
ences, adressees a M. de Voltaire, par M. Bailly. 1 London and 
Paris, 1779, 8vo. 

I might enter here all Bailly's histories of astronomy. 2 
The paradox which runs through them all more or less, is 
the doctrine that astronomy is of immense antiquity, com- 
ing from some forgotten source, probably the drowned island 
of Plato, peopled by a race whom Bailly makes, as has 

'Richard Lovett (1692-1780) was a good deal of a charlatan. 
He claimed to have studied electrical phenomena, and in 1758 ad- 
vertised that he could effect marvelous cures, especially of sore 
throat, by means of electricity. Before publishing the works men- 
tioned by De Morgan he had issued others of similar character, 
including The Subtile Medium proved (London, 1756) and The 
Reviewers Reviewed (London, 1760). 

1 Jean Sylvain Bailly (1736-1793), member of the Academic 
francaise and of the Academic des sciences, first deputy elected to 
represent Paris in the Etats-generaux (1789), president of the first 
National Assembly, and mayor of Paris (1789-1791). For his vigor 
as mayor in keeping the peace, and for his manly defence of the 
Queen, he was guillotined. He was an astronomer of ability, but 
is best known for his histories of the science. 

'These were the Histoire de T Astronomic ancienne (1775), His- 
toire de V Astronomic moderne (1778-1783), Histoire de I'Astronomie 
indienne et orientale (1787), and Lettres sur ? origin* des peuples de 
I'Asie (1775). 



SAINT-MARTIN ON ERRORS AND TRUTH. 167 

been said, to teach us everything except their existence and 
their name. These books, the first scientific histories which 
belong to readable literature, made a great impression by 
power of style: Delambre created a strong reaction, of in- 
jurious amount, in favor of history founded on contemporary 
documents, which early astronomy cannot furnish. These 
letters are addressed to Voltaire, and continue the discussion. 
There is one letter of Voltaire, being the fourth, dated Feb. 
27, 1777, and signed "le vieux malade de Ferney, V. puer 
centum annorum."3 Then begin Bailly's letters, from Jan- 
uary 16 to May 12, 1778. From some ambiguous expres- 
sions in the Preface, it would seem that these are fictitious 
letters, supposed to be addressed to Voltaire at their dates. 
Voltaire went to Paris February 10, 1778, and died there 
May 30. Nearly all this interval was his closing scene, and 
it is very unlikely that Bailly would have troubled him with 
these letters.* 

An inquiry into the cause of motion, or a general theory of 
physics. By S. Miller. London, 1781, 4to. 

Newton all wrong: matter consists of two kinds of par- 
ticles, one inert, the other elastic and capable of expanding 
themselves ad infinitum. 

SAINT-MARTIN ON ERRORS AND TRUTH. 

Des Erreurs et de la Verite, ou les hommes rappeles au prih- 
cipe universel de la science; ouvrage dans lequel, en faisant 
remarquer aux observateurs 1'incertitude de leurs recherches, 
et leurs meprises continuelles, on leur indique la route qu'ils 
auroient du suivre, pour acquerir 1'evidence physique sur 
Torigine du bien et du mal, sur 1'homme, sur la nature mate- 
rielle, et la nature sacree; sur la base des gouvernements 

"The sick old man of Ferney, V., a boy of a hundred years." 
Voltaire was born in 1694, and hence was eighty-three at this time. 

4 In Palmezeaux's Vie de Bailly, in Bailly's Ouvrage Posthume 
(1810), M. de Sales is quoted as saying that the Lettres sur I'Atlan- 
tide were sent to Voltaire and that the latter did not approve of the 
theory set forth. 



168 A BUDGET OF PARADOXES. 

politiques, sur 1'autorite des souverains, sur la justice civile 
et criminelle, sur les sciences, les langues, et les arts. Par 
un Ph.... Inc A Edimbourg. I782. 1 Two vols. 8vo. 

This is the famous work of Louis Claude de Saint- 
Martin 2 (1743-1803), for whose other works, vagaries in- 
cluded, the reader must look elsewhere : among other things, 
he was a translator of Jacob Behmen.3 The title promises 
much, and the writer has smart thoughts now and then ; 
but the whole is the wearisome omniscience of the author's 
day and country, which no reader of our time can tolerate. 
Not that we dislike omniscience ; but we have it of our own 
country, both home-made and imported ; and fashions vary. 
But surely there can be but one omniscience? Must a man 
have but one wife? Nay, may not a man have a new wife 
while the old one is living? There was a famous instru- 
mental professor forty years ago, who presented a friend 

to Madame . The friend started, and looked surprised ; 

for, not many weeks before, he had been presented to another 
lady, with the same title, at Paris. The musician observed 
his surprise, and quietly said, "Celle-ci est Madame - 
de Londres." In like manner we have a London omniscience 
now current, which would make any one start who only 
knew the old French article. 

The book was printed at Lyons, but it was a trick of 
French authors to pretend to be afraid of prosecution: it 

1 The British Museum catalogue gives two editions, 1781 and 
1782. 

a A mystic and a spiritualist. His chief work was the one men- 
tioned here. 

3 Jacob Behmen, or Bohme (1575-1624), known as "the German 
theosophist," was founder of the sect of Boehmists, a cult allied 
to the Swedenborgians. He was given to the study of alchemy, 
and brought the vocabulary of the science into his mystic writings. 
His sect was revived in England in the eighteenth century through 
the efforts of William Law. Saint-Martin translated into French 
two of his Latin works under the titles L'Aurore naissante, ou la 
Racine de la philosophie (1800), and Les trois principes de V essence 
divine (1802). The originals had appeared nearly two hundred 
years earlier, Aurora in 1612, and De tribus principiis in 1619. 



SAINT-MARTIN ON ERRORS AND TRUTH. 169 

made a book look wicked-like to have a feigned place of 
printing, and stimulated readers. A Government which 
had undergone Voltaire would never have drawn its sword 
upon quiet Saint-Martin. To make himself look still worse, 
he was only ph[ilosophe] Inc. . . ., which is generally read 
Inconnu? but sometimes Incredule:* most likely the am- 
biguity was intended. There is an awful paradox about the 
book, which explains, in part, its leaden sameness. It is all 
about I'homme, I'homme, I'homme, 6 except as much as treats 
of les hommes, les hommes, les hommes ; 7 but not one single 
man is mentioned by name in its 500 pages. It reminds 
one of 

"Water, water everywhere, 
And not a drop to drink." 

Not one opinion of any other man is referred to, in the way 
of agreement or of opposition. Not even a town is men- 
tioned: there is nothing which brings a capital letter into 
the middle of a sentence, except, by the rarest accident, 
such a personification as Justice. A likely book to want an 
Edimbourg godfather ! 

Saint-Martin is great in mathematics. The number four 
essentially belongs to straight lines, and nine to curves. 
The object of a straight line is to perpetuate ad infinitum 
the production of a point from which it emanates. A circle 
O bounds the production of all its radii, tends to destroy 
them, and is in some sort their enemy. How is it possible 
that things so distinct should not be distinguished in their 
number as well as in their action? If this important ob- 
servation had been made earlier, immense trouble would 
have been saved to the mathematicians, who would have 
been prevented from searching for a common measure to 
lines which have nothing in common. But, though all 
straight lines have the number four, it must not be supposed 
that they are all equal, for a line is the result of its law and 

'"Unknown." ""Skeptical." 

8 "Man, man, man." 7 "Men, men, men." 



170 A BUDGET OF PARADOXES. 

its number; but though both are the same for all lines of 
a sort, they act differently, as to force, energy, and duration, 
in different individuals ; which explains all differences of 
length, etc. I congratulate the reader who understands this ; 
and I do not pity the one who does not. 

Saint-Martin and his works are now as completely for- 
gotten as if they had never been born, except so far as this, 
that some one may take up one of the works as of heretical 
character, and lay it down in disappointment, with the re- 
flection that it is as dull as orthodoxy. For a person who 
was once in some vogue, it would be difficult to pick out 
a more fossil writer, from Aa to Zypoeus, except, though 
it is unusual for (, ) to represent an interval of more 
than a year his unknown opponent. This opponent, in the 
very year of the Des Erreurs. . . .published a book in two 
parts with the same fictitious place of printing; 

Tableau Nature! des Rapports qui existent entre Dieu, I'Homme, 
et 1'Univers. A Edimbourg, 1782, 8vo. 8 

There is a motto from the Des Erreurs itself, "Expliquer 
les choses par I'homme, et non 1'homme par les choses. Des 

Erreurs et de la Verite, par un PH INC , p. 9." 9 

This work is set down in various catalogues and biographies 

as written by the PH INC himself. But it is not 

usual for a writer to publish two works in the same year, 
one of which takes a motto from the other. And the second 
work is profuse in capitals and italics, and uses Hebrew 
learning: its style differs much from the first work. The 
first work sets out from man, and has nothing to do with 
God: the second is religious and raps the knuckles of the 
first as follows: "Si nous voulons nous preserver de toutes 

8 It is interesting to read De Morgan's argument against Saint- 
Martin's authorship of this work. It is attributed to Saint-Martin 
both by the Biographic Universelle and by the British Museum Cata- 
logue, and De Morgan says by "various catalogues and biographies." 

' "To explain things by man and not man by things. On Errors 
and Truth, by a Ph.. . . Inc.. . ." 



A FORERUNNER OF THE METRIC SYSTEM. 171 

les illusions, et surtout des amorces de 1'orgueil par les- 
quelles I'homme est si souvent seduit, ne prenons jamais les 
hommes, mais tou jours Dieu pour notre terme de compa- 
raison." 10 The first uses four and nine in various ways, of 
which I have quoted one: the second says, "Et ici se trouve 
deja une explication des nombres qualre et neuf, qui ont 
peu embarrasse dans 1'ouvrage deja cite. L'homme s'est 
egare en allant de quatre a neuf . . . ." 11 The work cited is 
the Erreurs, etc., and the citation is in the motto, which is 
the text of the opposition sermon. 

A FORERUNNER OF THE METRIC SYSTEM. 

Method to discover the difference of the earth's diameters; 
proving its true ratio to be not less variable than as 45 is to 

46, and shortest in its pole's axis 174 miles likewise a 

method for fixing an universal standard for weights and meas- 
ures. By Thomas Williams. 1 London, 1788, 8vo. 

Mr. Williams was a paradoxer in his day, and proposed 
what was, no doubt, laughed at by some. He proposed 
the sort of plan which the French independently of course 
carried into effect a few years after. He would have the 
52d degree of latitude divided into 100,000 parts and each 
part a geographical yard. The geographical ton was to 
be the cube of a geographical yard filled with sea-water 
taken some leagues from land. All multiples and sub- 
divisions were to be decimal. 

I was beginning to look up those who had made similar 
proposals, when a learned article on the proposal of a 

9 "If we would preserve ourselves from all illusions, and above 
all from the allurements of pride, by which man is so often seduced, 
we should never take man, but always God, for our term of com- 
parison." 

1 "And here is found already an explanation of the numbers four 
and nine which caused some perplexity in the work cited above. 
Man is lost in passing from four to nine." 

1 Williams also took part in the preparation of some tables for 
the government to assist in the determination of longitude. He had 
published a work two years before the one here cited, on the same 
subject, An entire new work and method to discover the variation 
of the Earth's Diaameters, London, 1786. 



172 A BUDGET OF PARADOXES. 

metrical system came under my eye in the Times of Sept. 
15, 1863. The author cites Mouton, 2 who would have the 
minute of a degree divided into 10,000 virgulce', James 
Cassini,3 whose foot was to be six thousandths of a minute ; 
and Paucton,* whose foot was the 400,000th of a degree. I 
have verified the first and third statements ; surely the 
second ought to be the six-thousandth. 

An inquiry into the Copernican system. .. -wherein it is proved, 
in the clearest manner, that the earth has only her diurnal 

motion with an attempt to point out the only true way 

whereby mankind can receive any real benefit from the study 
of the heavenly bodies. By John Cunningham. 5 London, 
1789, 8vo. 

The "true way" appears to be the treatment of heaven 
and earth as emblematical of the Trinity. 

Cosmology. An inquiry into the cause of what is called gravi- 
tation or attraction, in which the motions of the heavenly 
bodies, and the preservation and operations of all nature, are 
deduced from an universal principle of efflux and reflux. By 
T. Vivian, 6 vicar of Cornwood, Devon. Bath, 1792, I2mo. 

2 This is Gabriel Mouton (1618-1694), a vicar at Lyons, who 
suggested as a basis for a natural system of measures the mille, 
a minute of a degree of the meridian. This appeared in his Ob- 
servationes diametrorum soils et lunae apparentium, meridianarum- 
que aliquot altitudinum cum tabula declinationum solis. . . . Lyons, 
1670. 

3 Jacques Cassini (1677-1756), one of the celebrated Cassini fam- 
ily of astronomers. After the death of his father he became director 
of the observatory at Paris. The basis for a metric unit was set 
forth by him in his Traite de la grandeur et de la figure de la terre, 
Paris, 1720. He was a prolific writer on astronomy. 

* Alexis Jean Pierre Paucton (1732-1798). He was, for a time, 
professor of mathematics at Strassburg, but later (1796) held office 
in Paris. His leading contribution to metrology was his Metrologie 
ou Traite des mesures, Paris, 1780. 

8 He was an obscure writer, born at Deptford. 

"He was also a writer of no scientific merit, his chief contribu- 
tions being religious tracts. One of his productions, however, went 
through many editions, even being translated into French, Three 
dialogues between a Minister and one of his Parishioners; on the 
true principles of Religion and salvation for sinners by Jesus Christ. 
The twentieth edition appeared at Cambridge in 1786. 



173 



Attraction, an influx of matter to the sun ; centrifugal 
force, the solar rays ; cohesion, the pressure of the atmos- 
phere. The confusion about centrifugal force, so called, as 
demanding an external agent, is very common. 

THOMAS PAINE'S RIGHTS OF MAN. 

The rights of MAN, being an answer to Mr. Burke's attack on 
the French Revolution. 1 By Thomas Paine. 2 In two parts. 
1791-1792. 8vo. (Various editions.) 3 

A vindication of the rights of WOMAN, with strictures on polit- 
ical and moral subjects. By Mary Wollstonecraft. 4 1792. Svo. 

A sketch of the rights of BOYS and GIRLS. By Launcelot Light, 
of Westminster School; and Lsetitia Lookabout, of Queen's 
Square, Bloomsbury. [By the Rev. Samuel Parr, 5 LL.D.] 
1792. 8vo. (pp.64). 

When did we three meet before? The first work has 
sunk into oblivion: had it merited its title, it might have 

1 This was the Reflections on the Revolution in France, and on 
the proceedings in certain societies in London relative to that event 
(London, 1790) by Edmund Burke (1729-1797). Eleven editions 
of the work appeared the first year. 

2 Paine (1736-1809) was born in Norfolkshire, of Quaker par- 
ents. He went to America at the beginning of the Revolution and 
published, in January 1776, a violent pamphlet entitled Common Sense. 
He was a private soldier under Washington, and on his return to 
England after the war he published The Rights of Man. He was 
indicted for treason and was outlawed to France. He was elected 
to represent Calais at the French convention, but his plea for mod- 
eration led him perilously near the guillotine. His Age of Reason 
(1794) was dedicated to Washington. He returned to America in 
1802 and remained there until his death. 

8 Part I appeared in 1791 and was so popular that eight editions 
appeared in that year. It was followed in 1792 by Part II, of which 
nine editions appeared in that year. Both parts were immediately 
republished in Paris, and there have been several subsequent edi- 
tions. 

*Mary Wollstonecraft (i759-i797) was only thirty-three when 
this work came out She had already published An historical and 
moral View of the Origin and Progress of the French Revolution 
(1790), and Original Stories from Real Life (1791). She went to 
Paris in 1792 and remained during the Reign of Terror. 

6 Samuel Parr (1747-1827) was for a time head assistant at 
Harrow (1767-1771), and afterwards headmaster in other schools. 
At the time this book was written he was vicar of Hatton, where he 
took private pupils (1785-1798) to the strictly limited number of 
seven. He was a violent Whig and a caustic writer. 



174 A BUDGET OF PARADOXES. 

lived. It is what the French call a piece de circonstance ; it 
belongs in time to the French Revolution, and in matter to 
Burke's opinion of that movement. Those who only know 
its name think it was really an attempt to write a philosoph- 
ical treatise on what we now call socialism. Silly govern- 
ment prosecutions gave it what it never could have got for 
itself. 

Mary Wollstonecraft seldom has her name spelled right. 
I suppose the O ! O ! character she got made her Waolstone- 
craft. Watt gives double insinuation, for his cross-reference 
sends us to Goodwin. 6 No doubt the title of the book was 
an act of discipleship to Paine's Rights of Man ; but this 
title is very badly chosen. The book was marred by it, 
especially when the authoress and her husband assumed the 
right of dispensing with legal sanction until the approach of 
offspring brought them to a sense of their child's interest.? 
Not a hint of such a claim is found in the book, which is 
mostly about female education. The right claimed for wo- 
man is to have the education of a rational human being, 
and not to be considered as nothing but woman throughout 
youthful training. The maxims of Mary Wollstonecraft are 
now, though not derived from her, largely followed in the 
education of girls, especially in home education: just as 
many of the political principles of Tom Paine, again not 
derived from him, are the guides of our actual legislation. 
I remember, forty years ago, an old lady used to declare 
that she disliked girls from the age of sixteen to five-and- 
twenty. "They are full," said she, "of femalities." She 
spoke of their behavior to women as well as to men. She 

9 On Mary Wollstonecraft's return from France she married 
(1797) William Godwin (1756-1836). He had started as a strong 
Calvinistic Nonconformist minister, but had become what would now 
be called an anarchist, at least by conservatives. He had written an 
Inquiry concerning Political Justice (1793) and a novel entitled 
Caleb Williams, or Things as they are (1794), both of which were 
of a nature to attract his future wife. 

T This child was a daughter. She became Shelley's wife, and 
Godwin's influence on Shelley was very marked. 



THOMAS PAINE'S RIGHTS OF MAN. 175 

would have been shocked to know that she was a follower 
of Mary Wollstonecraft, and had packed half her book into 
one sentence. 

The third work is a satirical attack on Mary Wollstone- 
craft and Tom Paine. The details of the attack would con- 
vince any one that neither has anything which would now 
excite reprobation. It is utterly unworthy of Dr. Parr, and 
has quite disappeared from lists of his works, if it were ever 
there. That it was written by him I take to be evident, as 
follows. Nichols, 8 who could not fail to know, says (Anecd., 
vol. ix, p. 120) : "This is a playful essay by a first-rate 
scholar, who is elsewhere noticed in this volume, but whose 
name I shall not bring forward on so trifling an occasion." 
Who the scholar was is made obvious by Master Launcelot 
being made to talk of Bellendenus.9 Further, the same boy 
is made to say, "Let Dr. Parr lay his hand upon his heart, 
if his conscience will let him, and ask himself how many 
thousands of wagon-loads of this article [birch] he has 
cruelly misapplied." How could this apply to Parr, with his 
handful of private pupils, 10 and no reputation for severity? 
Any one except himself would have called on the head- 
master of Westminster or Eton. I doubt whether the name 
of Parr could be connected with the rod by anything in 
print, except the above and an anecdote of his pupil, Tom 
Sheridan. 11 The Doctor had dressed for a dinner visit, and 

8 This was John Nichols (1745-1826), the publisher and anti- 
quary. He edited the Gentleman's Magazine (1792-1826) and his 
works include the Literary Anecdotes of the Eighteenth Century 
(1812-1815), to which De Morgan here refers. 

9 William Bellenden, a Scotch professor at the University of 
Paris, who died about 1633. His textbooks are now forgotten, but 
Parr edited an edition of his works in 1787. The Latin preface, 
Pracfatio ad Bellendum de Statu, was addressed to Burke, North, 
and Fox, and was a satire on their political opponents. 

10 As we have seen, he had been head-master before he began 
taking "his handful of private pupils." 

11 The story has evidently got mixed up in the telling, for Tom 
Sheridan (1721-1788), the great actor, was old enough to have been 
Dr. Parr's father. It was his son, Richard Brinsley Sheridan (1751- 
1816), the dramatist and politician, who was the pupil of Parr. He 



176 A BUDGET OF PARADOXES. 

was ready a quarter of an hour too soon to set off. "Tom," 
said he, "I think I had better whip you now ; you are sure to 
do something while I am out." "I wish you would, sir!" 
said the boy ; "it would be a letter of licence for the whole 
evening." The Doctor saw the force of the retort: my two 
tutelaries will see it by this time. They paid in advance; 
and I have given liberal interpretation to the order. 

The following story of Dr. Parr was told me and 
others, about 1829, by the late Leonard Horner, 12 who knew 
him intimately. Parr was staying in a house full of com- 
pany, I think in the north of England. Some gentlemen 
from America were among the guests, and after dinner they 
disputed some of Parr's assertions or arguments. So the 
Doctor broke out with "Do you know what country you 
come from? You come from the place to which we used 
to send our thieves!" This made the host angry, and he 
gave Parr such a severe rebuke as sent him from the room 
in ill-humor. The rest walked on the lawn, amusing the 
Americans with sketches of the Doctor. There was a dark 
cloud overhead, and from that cloud presently came a voice 
which called Tham (Parr-lisp for Sam). The company 
were astonished for a moment, but thought the Doctor was 
calling his servant in the house, and that the apparent direc- 
tion was an illusion arising out of inattention. But presently 
the sound was repeated, certainly from the cloud, 

"And nearer, clearer, deadlier than before." 

There was now a little alarm : where could the Doctor have 
got to? They ran to his bedroom, and there they discovered 
a sufficient rather than satisfactory explanation. The Doctor 
had taken his pipe into his bedroom, and had seated himself, 
in sulky mood, upon the higher bar of a large and deep old- 
fashioned grate with a high mantelshelf. Here he had turn- 
wrote The Rivals (1775) and The School for Scandal (1777) soon 
after Parr left Harrow. 

"Horner (1785-1864) was a geologist and social reformer. He 
was very influential in improving the conditions of child labor. 



ATTACKS ON RELIGIOUS CUSTOMS. 177 

bled backwards, and doubled himself up between the bars 
and the back of the grate. He was fixed tight, and when 
he called for help, he could only throw his voice up the 
chimney. The echo from the cloud was the warning which 
brought his friends to the rescue. 

ATTACKS ON RELIGIOUS CUSTOMS. 

Days of political paradox were coming, at which we now 
stare. Cobbett 1 said, about 1830, in earnest, that in the 
country every man who did not take off his hat to the 
clergyman was suspected, and ran a fair chance of having 
something brought against him. I heard this assertion can- 
vassed, when it was made, in a party of elderly persons. 
The Radicals backed it, the old Tories rather denied it, 
but in a way which satisfied me they ought to have denied 
it less if they could not deny it more. But it must be said 
that the Governments stopped far short of what their parti- 
sans would have had them do. All who know Robert Robin- 
son's 2 very quiet assault on church-made festivals in his 
History and Mystery of Good Friday (1777)3 will hear or 
remember with surprise that the British Critic pronounced 
it a direct, unprovoked, and malicious libel on the most 

1 William Cobbett (1762-1835), the journalist, was a character 
not without interest to Americans. Born in Surrey, he went to 
America at the age of thirty and remained there eight years. Most 
of this time he was occupied as a bookseller in Philadelphia, and 
while thus engaged he was fined for libel against the celebrated Dr. 
Rush. On his return to England he edited the Weekly Political 
Register (1802-1835), a popular journal among the working classes. 
He was fined and imprisoned for two years because of his attack 
(1810) on military flogging, and was also (1831) prosecuted for 
sedition. He further showed his paradox nature by his History of 
the Protestant Reformation (1824-1827), an attack on the prevail- 
ing Protestant opinion. He also wrote a Life of Andrew Jackson 
(1834). After repeated attempts he succeeded in entering parlia- 
ment, a result of the Reform Bill. 

'Robinson (1735-1790) was a Baptist minister who wrote sev- 
eral theological works and a number of hymns. His work at Cam- 
bridge so offended the students that they at one time broke up the 
services. 

8 This work had passed through twelve editions by 1823. 



178 A BUDGET OF PARADOXES. 

sacred institutions of the national Church. It was reprinted 
again and again: in 1811 it was in a cheap form at 6s. 6d. 
a hundred. When the Jacobin day came, the State was 
really in a fright: people thought twice before they pub- 
lished what would now be quite disregarded. I examined 
a quantity of letters addressed to George Dyer4 (Charles 
Lamb's G.D.) and what between the autographs of Thel- 
wall, Hardy, Home Tooke, and all the rebels,* put together 
a packet which produced five guineas, or thereabouts, for 
the widow. Among them were the following verses, sent 
by the author who would not put his name, even in a pri- 
vate letter, for fear of accidents for consultation whether 
they could safely be sent to an editor: and they were not 
sent. The occasion was the public thanksgiving at St. Paul's 
for the naval victories, December 19, 1797. 

"God bless me! what a thing! 
Have you heard that the King 
Goes to St. Paul's? 

4 Dyer (1755-1841), the poet and reformer, edited Robinson's 
Ecclesiastical Researches (1790). He was a life-long friend of 
Charles Lamb, and in their boyhood they were schoolmates at 
Christ's Hospital. His Complaints of the Poor People of England 
(1793) made him a worthy companion of the paradoxers above 
mentioned. 

8 These were John Thelwall (1764-1834) whose Politics for the 
People or Hogswash (1794) took its title from the fact that Burke 
called the people the "swinish multitude." The book resulted in send- 
ing the author to the Tower for sedition. In 1798 he gave up poli- 
tics and start a school of elocution which became very famous. 
Thomas Hardy (1752-1832), who kept a bootmaker's shop in Picca- 
dilly, was a fellow prisoner with Thelwall, being arrested for high 
treason. He was founder (1792) of The London Corresponding 
Society, a kind of clearing house for radical associations throughout 
the country. Home Tooke was really John Home (1736-1812), he 
having taken the name of his friend William Tooke in 1782. He 
was a radical of the radicals, and organized a number of reform 
societies. Among these was the Constitutional Society that voted 
money (1775) to assist the American revolutionists, appointing him 
to give the contribution to Franklin. For this he was imprisoned 
for a year. With his fellow rebels in the Tower in 1794, however, 
he was acquitted. As a philologist he is known for his early ad- 
vocacy of the study of Anglo-Saxon and Gothic, and his Diversions 
of Purley ( 1786) is still known to readers. 



ATTACKS ON RELIGIOUS CUSTOMS. 179 

Good Lord ! and when he's there, 
He'll roll his eyes in prayer, 
To make poor Johnny stare 
At this fine thing. 

"No doubt the plan is wise 
To blind poor Johnny's eyes 

By this grand show; 
For should he once suppose 
That he's led by the nose, 
Down the whole fabric goes, 

Church, lords, and king. 

"As he shouts Duncan's 6 praise, 
Mind how supplies they'll raise 

In wondrous haste. 
For while upon the sea 
We gain one victory, 
John still a dupe will be 

And taxes pay. 

"Till from his little store 
Three-fourths or even more 

Goes to the Crown. 
Ah, John! you little think 
How fast we downward sink 
And touch the fatal brink 

At which we're slaves." 

I would have indicted the author for not making his 
thirds and sevenths rhyme. As to the rhythm, it is not 
much better than what the French sang in the Calais theater 
when the Duke of Clarence? took over Louis XVIII in 1814. 

"God save noble Clarence, 
Who brings our king to France ; 

God save Clarence ! 
He maintains the glory 
Of the British navy, 
etc., etc." 

"This was the admiral, Adam Viscount Duncan (1731-1804), 
who defeated the Dutch off Camperdown in 1797. 

7 He was created Duke of Clarence and St. Andrews in 1789 
and was Admiral of the Fleet escorting Louis XVIII on his return 



180 A BUDGET OF PARADOXES. 

Perhaps had this been published, the Government would 
have assailed it as a libel on the church service. They got 
into the way of defending themselves by making libels on 
the Church, of what were libels, if on anything, on the 
rulers of the State ; until the celebrated trials of Hone 
settled the point for ever, and established that juries will 
not convict for one offence, even though it have been com- 
mitted, when they know the prosecution is directed at an- 
other offence and another intent. 

HONE'S FAMOUS TRIALS. 

The results of Hone's trials (William Hone, 1779-1842) 
are among the important constitutional victories of our cen- 
tury. He published parodies on the Creeds, the Lord's 
Prayer, the Catechism, etc., with intent to bring the Ministry 
into contempt: everybody knew that was his purpose. The 
Government indicted him for impious, profane, blasphemous 
intent, but not for seditious intent. They hoped to wear 
him out by proceeding day by day. December 18, 1817, 
they hid themselves under the Lord's Prayer, the Creed, 
and the Commandments ; December 19, under the Litany ; 
December 20, under the Athanasian Creed, an odd place for 
shelter when they could not find it in the previous places. 
Hone defended himself for six, seven, and eight hours on 
the several days: and the jury acquitted him in 15, 105, and 
20 minutes. In the second trial the offense was laid both 
as profanity and as sedition, which seems to have made the 
jury hesitate. And they probably came to think that the 
second count was false pretence : but the length of their de- 
liberation is a satisfactory addition to the value of the whole. 
In the first trial the Attorney-General (Shepherd) had the 
impudence to say that the libel had nothing of a political 
tendency about it, but was avowedly set off against the 
religion and worship of the Church of England. The whole 

to France in 1814. He became Lord High Admiral in 1827, and 
reigned as William IV from 1830 to 1837. 



HONE'S FAMOUS TRIALS. 181 

is political in every sentence ; neither more nor less political 
than the following, which is part of the parody on the Cat- 
echism: "What is thy duty towards the Minister? My duty 
towards the Minister is, to trust him as much as I can; to 
honor him with all my words, with all my bows, with all 
my scrapes, and with all my cringes ; to flatter him ; to give 
him thanks; to give up my whole soul to him; to idolize 
his name, and obey his word, and serve him blindly all the 
days of his political life." And the parody on the Creed 
begins, "I believe in George, the Regent almighty, maker 
of new streets and Knights of the Bath." This is what the 
Attorney-General said had nothing of a political tendency 
about it. But this was on the first trial: Hone was not 
known. The first day's trial was under Justice Abbott 
(afterwards C. J. Tenterden). 1 It was perfectly understood, 
when Chief Justice Ellenborough 2 appeared in Court on the 
second day, that he was very angry at the first result, and 
put his junior aside to try his own rougher dealing. But 
Hone tamed the lion. An eye-witness told me that when 
he implored of Hone not to detail his own father Bishop 
Law'ss views on the Athanasian Creed, which humble peti- 
tion Hone kindly granted, he held by the desk for support. 
And the same when which is not reported the Attorney- 
General appealed to the Court for protection against a 

1 This was Charles Abbott (1762-1832) first Lord Tenterden. 
He succeeded Lord Ellenborough as Chief Justice (1818) and was 
raised to the peerage in 1827. He was a strong Tory and opposed 
the Catholic Relief Bill, the Reform Bill, and the abolition of the 
death penalty for forgery. 

'Edward Law (1750-1818), first Baron Ellenborough. He was 
chief counsel for Warren Hastings, and his famous speech in de- 
fense of his client is well known. He became Chief Justice and was 
raised to the peerage in 1802. He opposed all efforts to modernize 
the criminal code, insisting upon the reactionary principle of new 
death penalties. 

"Edmund Law (1703-1787), Bishop of Carlisle (1768), was a 
good deal more liberal than his son. His Considerations on the 
Propriety of requiring subscription to the Articles of Faith (1774) 
was published anonymously. In it he asserts that not even the 
clergy should be required to subscribe to the thirty-nine articles. 



182 A BUDGET OF PARADOXES. 

stinging attack which Hone made on the Bar: he held on, 
and said, "Mr. Attorney, what can I do!" I was a boy of 
twelve years old, but so strong was the feeling of exultation 
at the verdicts that boys at school were not prohibited from 
seeing the parodies, which would have been held at any 
other time quite unfit to meet their eyes. I was not able 
to comprehend all about the Lord Chief Justice until I read 
and heard again in after years. In the meantime, Joe Miller 
had given me the story of the leopard which was sent home 
on board a ship of war, and was in two days made as docile 
as a cat by the sailors/ "You have got that fellow well 
under," said an officer. "Lord bless your Honor!" said 
Jack, "if the Emperor of Marocky would send us a cock 
rhinoceros, we'd bring him to his bearings in no time!" 
When I came to the subject again, it pleased me to enter- 
tain the question whether, if the Emperor had sent a cock 
rhinoceros to preside on the third day in the King's Bench, 
Hone would have mastered him: I forget how I settled it. 
There grew up a story that Hone caused Lord Ellenbor- 
ough's death, but this could not have been true. Lord Ellen- 
borough resigned his seat in a few months, and died just 
a year after the trials ; but sixty-eight years may have had 
more to do with it than his defeat. 

A large subscription was raised for Hone, headed by 
the Duke of Bedford* for 105. Many of the leading anti- 
ministerialists joined : but there were many of the other side 
who avowed their disapprobation of the false pretense. 
Many could not venture their names. In the list I find: 

/Joe Miller (1684-1738), the famous Drury Lane comedian, was 
so illiterate that he could not have written the Joe Miller's Jests, or 
the Wit's Vade-Mecum that appeared the year after his death. It 
was often reprinted and probably contained more or less of Miller's 
own jokes. 

6 The sixth duke (1766-1839) was much interested in parliamen- 
tary reform. He was a member of the Society of Friends of the 
People. He was for fourteen years a member of parliament (1788- 
1802) and was later Lord Lieutenant of Ireland (1806-1807). He 
afterwards gave up politics and became interested in agricultural 
matters. 



HONE'S FAMOUS TRIALS. 183 

A member of the House of Lords, an enemy to persecution, 
and especially to religious persecution employed for political 
purposes No parodist, but an enemy to persecution A 
juryman on the third day's trial Ellen Borough My name 
would ruin me Oh ! minions of Pitt Oil for the Hone 
The Ghosts of Jeffries 6 and Sir William Roy [Ghosts of 
Jeffries in abundance] A conscientious Jury and a con- 
scientious Attorney, 1 6s. 8d. To Mr. Hone, for defend- 
ing in his own person the freedom of the press, attacked 
for a political object, under the old pretense of supporting 
Religion A cut at corruption An Earldom for myself 
and a translation for my brother One who disapproves of 
parodies, but abhors persecution From a schoolboy who 
wishes Mr. Hone to have a very grand subscription "For 
delicacy's sake forbear/ 5 and "Felix trembled" "I will go 
myself to-morrow" Judge Jeffries' works rebound in calf 
by Law Keep us from Law, and from the Shepherd's 
paw I must not give you my name, but God bless you! 
As much like Judge Jeffries as the present times will permit 
May Jeffries' fame and Jeffries' fate on every modern 
Jeffries wait No parodist, but an admirer of the man who 
has proved the fallacy of the Lawyer's Law, that when a 
man is his own advocate he has a fool for his client A 
Mussulman who thinks it would not be an impious libel to 
parody the Koran May the suspenders of the Habeas 
Corpus Act be speedily suspended Three times twelve for 
thrice-tried Hone, who cleared the cases himself alone, 
and won three heats by twelve to one, 1 16s. A conscien- 
tious attorney, i\ 6s. 8d. Rev. T. B. Morris, rector of 
Shelf anger, who disapproves of the parodies, but abhors 
the making an affected zeal for religion the pretext for 
political persecution A Lawyer opposed in principle to 

'George Jeffreys (c. 1648-1689), the favorite of James II, who 
was active in prosecuting the Rye House conspirators. He was 
raised to the peerage in 1684 and held the famous "bloody assize" 
in the following year, being made Lord Chancellor as a result. He 
was imprisoned in the Tower by William III and died there. 



184 A BUDGET OF PARADOXES. 

Law For the Hone that set the razor that shaved the rats 
Rev. Dr. Samuel Parr, who most seriously disapproves 
of all parodies upon the hallowed language of Scripture 
and the contents of the Prayer-book, but acquits Mr. Hone 
of intentional impiety, admires his talents and fortitude, 
and applauds the good sense and integrity of his juries 
Religion without hypocrisy, and Law without impartiality 
O Law ! O Law ! O Law ! 

These are specimens of a great many allusive mottoes. 
The subscription was very large, and would have bought 
a handsome annuity, but Hone employed it in the bookselling 
trade, and did not thrive. His Everyday Book 7 and his Apoc- 
ryphal New Testament? are useful books. On an annuity 
he would have thriven as an antiquarian writer and collec- 
tor. It is well that the attack upon the right to ridicule 
Ministers roused a dormant power which was equal to the 
occasion. Hone declared, on his honor, that he had never 
addressed a meeting in his life, nor spoken a word before 
more than twelve persons. Had he which however could 
not then be done employed counsel and had a guilty de- 
fense made for him, he would very likely have been con- 
victed, and the work would have been left to be done by 
another. No question that the parodies disgusted all who 
reverenced Christianity, and who could not separate the 
serious and the ludicrous, and prevent their existence in 
combination. 

My extracts, etc., are from the nineteenth, seventeenth, 
and sixteenth editions of the three trials, which seem to have 
been contemporaneous (all in 1818) as they are made up 
into one book, with additional title over all, and the motto 
"Thrice the brindled cat hath mew'd." They are published 
by Hone himself, who I should have said was a publisher 

T The Every Day Book, forming a Complete History of the Year, 
Months, and Seasons, and a perpetual Key to the Almanack, 1826- 
1827. 

8 The first and second editions appeared in 1820. Two others 
followed in 1821. 



HONE'S FAMOUS TRIALS. 185 

as well as was to be. And though the trials only ended 
Dec. 20, 1817, the preface attached to this common title is 
dated Jan. 23, 1818.9 

The spirit which was roused against the false dealing of 
the Government, i. e., the pretense of prosecuting for im- 
piety when all the world knew the real offense was, if any- 
thing, sedition was not got up at the moment: there had 
been previous exhibitions of it. For example, in the spring 
of 1818 Mr. Russell, a little printer in Birmingham, was 
indicted for publishing the Political Litany 10 on which Hone 
was afterwards tried. He took his witnesses to the summer 
Warwick assizes, and was told that the indictment had been 
removed by certiorari into the King's Bench. He had no- 
tice of trial for the spring assizes at Warwick : he took his 
witnesses there, and the trial was postponed by the Crown. 
He then had notice for the summer assizes at Warwick ; 
and so on. The policy seems to have been to wear out the 
obnoxious parties, either by delays or by heaping on trials. 
The Government was odious, and knew it could not get 
verdicts against ridicule, and could get verdicts against im- 
piety. No difficulty was found in convicting the sellers of 
Paine's works, and the like. When Hone was held to bail 
it was seen that a crisis was at hand. All parties in politics 
furnished him with parodies in proof of religious persons 
having made instruments of them. The parodies by Addi- 
son and Luther were contributed by a Tory lawyer, who was 
afterwards a judge. 

Hone had published, in 1817, tracts of purely political 
ridicule: Official Account of the Noble Lord's Bite, Trial of 
the Dog for Biting the Noble Lord, etc. These were not 
touched. After the trials, it is manifest that Hone was 

8 The three trials of W. H., for publishing three parodies; viz. 
the late John Wilkes' Catechism, the Political Litany, and the Sine- 
curist's Creed; on three ex-ofhcio informations, at Guildhall, London, 
Dec. 18, 19, & 20, 1817, London, 1818. 

10 The Political Litany appeared in 1817. 
"That is, Castlereagh's. 



186 A BUDGET OF PARADOXES. 

to be unassailed, do what he might. The Political House 
that Jack built, in 1819; The Man in the Moon, 1820; The 
Queen's Matrimonial Ladder, Non mi ricordo, The R / 
Fowls, 1820; The Political Showman at Home, with plates 
by G. Cruickshank, 12 1821 [he did all the plates] ; The Spirit 
of Despotism, 1821 would have been legitimate marks for 
prosecution in previous years. The biting caricature of sev- 
eral of these works are remembered to this day. The Spirit 
of Despotism was a tract of 1795, of which a few copies had 
been privately circulated with great secrecy. Hone reprinted 
it, and prefixed the following address to "Robert Stewart, 
alias Lord Castlereagh"^ : "It appears to me that if, un- 
happily, your counsels are allowed much longer to prevail 
in the Brunswick Cabinet, they will bring on a crisis, in 
which the king may be dethroned or the people enslaved. 
Experience has shown that the people will not be enslaved 
the alternative is the affair of your employers." Hone 
might say this without notice. 

In 1819 Mr. Murray 1 * published Lord Byron's Don Juan, 1 * 
and Hone followed it with Don John, or Don Juan Un- 
masked, a little account of what the publisher to the Ad- 
miralty was allowed to issue without prosecution. The 
parody on the Commandments was a case very much in 
point : and Hone makes a stinging allusion to the use of the 
"unutterable Name, with a profane levity unsurpassed by 

12 The well-known caricaturist (1792-1878), then only twenty-nine 
years old. 

"Robert Stewart (1769-1822) was second Marquis of London- 
derry and Viscount Castlereagh. As Chief Secretary for Ireland 
he was largely instrumental in bringing about the union of Ireland 
and Great Britain. He was at the head of the war department dur- 
ing most of the Napoleonic wars, and was to a great extent respon- 
sible for the European coalition against the Emperor. He suicided 
in 1822. 

"John Murray (1778-1843), the well-known London publisher. 
He refused to finish the publication of Don Juan, after the first five 
cantos, because of his Tory principles. 

"Only the first two cantos appeared in 1819. 



HONE'S FAMOUS TRIALS. 187 

any other two lines in the English language." The lines 
are 

'"Tis strange the Hebrew noun which means 'I am/ 
The English always use to govern d n." 

Hone ends with : "Lord Byron's dedication of 'Don Juan' to 
Lord Castlereagh was suppressed by Mr. Murray from deli- 
cacy to Ministers. Q. Why did not Mr. Murray suppress Lord 
Byron's parody on the Ten Commandments? A. Because 
it contains nothing in ridicule of Ministers, and therefore 
nothing that they could suppose would lead to the displeas- 
ure of Almighty God." 

The little matters on which I have dwelt will never ap- 
pear in history from their political importance, except in a 
few words of result. As a mode of thought, silly evasions 
of all kinds belong to such a work as the present. Ignorance, 
which seats itself in the chair of knowledge, is a mother 
of revolutions in politics, and of unread pamphlets in circle- 
squaring. From 1815 to 1830 the question of revolution or 
no revolution lurked in all our English discussions. The 
high classes must govern ; the high classes shall not govern ; 
and thereupon issue was to be joined. In 1828-33 the ques- 
tion came to issue; and it was, Revolution with or without 
civil war; choose. The choice was wisely made; and the 
Reform Bill started a new system so well dovetailed into 
the old that the joinings are hardly visible. And now, in 
1867, the thing is repeated with a marked subsidence of 
symptoms ; and the party which has taken the place of the 
extinct Tories is carrying through Parliament a wider ex- 
tension of the franchise than their opponents would have ven- 
tured. Napoleon used to say that a decided nose was a sign 
of power: on which it has been remarked that he had good 
reason to say so before the play was done. And so had 
our country ; it was saved from a religious war, and from 
a civil war, by the power of that nose over its colleagues. 



188 A BUDGET OF PARADOXES. 

THOMAS TAYLOR, THE PLATONIST. 

The Commentaries of Proclus. 1 Translated by Thomas Taylor. 2 
London, 1792, 2 vols. 4to. 3 

The reputation of "the Platonist" begins to grow, and 
will continue to grow. The most authentic account is in 
the Penny Cyclopaedia, written by one of the few persons 
who knew him well, and one of the fewer who possess all 
his works. At page Ivi of the Introduction is Taylor's no- 
tion of the way to find the circumference. It is not geo- 
metrical, for it proceeds on the motion of a point : the words 
"on account of the simplicity of the impulsive motion, such 
a line must be either straight or circular" will suffice to 
show how Platonic it is. Taylor certainly professed a kind 
of heathenism. D'Israeli said, "Mr. T. Taylor, the Platonic 
philosopher and the modern Plethon, 4 consonant to that phi- 
losophy, professes polytheism." Taylor printed this in large 
type, in a page by itself after the dedication, without any dis- 
avowal. I have seen the following, Greek and translation 
both, in his handwriting: "lias dyaflos fj ayaObs c0nKos- /cat Tras 
XpicTTiavos y ;(/3mavos /caicos. Every good man, so far as he 
is a good man, is a heathen ; and every Christian, so far as 
he is a Christian, is a bad man." Whether Taylor had in his 
head the Christian of the New Testament, or whether he 
drew from those members of the "religious world" who 
make manifest the religious flesh and the religious devil, 

* Proclus (412-485), one of the greatest of the neo-Platonists, 
studied at Alexandria and taught philosophy at Athens. He left 
commentaries on Plato and on part of Euclid's Elements. 

3 Thomas Taylor (1758-1835), called "the Platonist," had a lik- 
ing for mathematics, and was probably led by his interest in number 
mysticism to a study of neo-Platonism. He translated a number of 
works from the Latin and Greek, and wrote two works on theoretical 
arithmetic (1816, 1823). 

'There was an earlier edition, 1788-89. 

*Georgius Gemistus, or Georgius Pletho (Plethon), lived in 
the fourteenth and fifteenth centuries. He was a native of Constan- 
tinople, but spent most of his time in Greece. He devoted much 
time to the propagation of the Platonic philosophy, but also wrote on 
divinity, geography, and history. 



A NEW ERA IN FICTION. 189 

cannot be decided by us, and perhaps was not known to 
himself. If a heathen, he was a virtuous one. 

A NEW ERA IN FICTION. 

(1795.) This is the date of a very remarkable paradox. 
The religious world to use a name claimed by a doctrinal 
sect had long set its face against amusing literature, and 
all works of imagination. Bunyan, Milton, and a few others 
were irresistible ; but a long face was pulled at every at- 
tempt to produce something readable for poor people and 
poor children.' In 1795, a benevolent association began to 
circulate the works of a lady who had been herself a drama- 
tist, and had nourished a pleasant vein of satire in the so- 
ciety of Garrick and his friends ; all which is carefully sup- 
pressed in some biographies. r Hannah MoreV Cheap Re- 
pository Tracts, 2 which were bought by millions of copies, 
destroyed the vicious publications with which the hawkers 
deluged the country, by the simple process of furnishing 
the hawkers with something more saleable. 1 

Dramatic fiction, in which the characters are drawn by 
themselves, was, at the middle of the last century, the mo- 
nopoly of writers who required indecorum, such as Fielding 
and Smollett. All, or nearly all, which could be permitted 
to the young, was dry narrative, written by people who could 
not make their personages talk character; they all spoke 

1 Hannah More (1745-1833), was, in her younger days, a friend 
of Burke, Reynolds, Dr. Johnson, and Garrick. At this time she 
wrote a number of poems and aspired to become a dramatist. Her 
Percy (1777), with a prologue and epilogue by Garrick, had a long 
run at Covent Garden. Somewhat later she came to believe that 
the playhouse was a grave public evil, and refused to attend the 
revival of her own play with Mrs. Siddons in the leading part. 
After 1789 she and her sisters devoted themselves to starting schools 
for poor children, teaching them religion and housework, but leaving 
them illiterate. 

2 These were issued at the rate of three each month, a story, a 
ballad, and a Sunday tract. They were collected and published in 
one volume in 1795. It is said that two'million copies were sold the 
first year. There were also editions in 1798, 1819, 1827, and 1836-37. 



190 A BUDGET OF PARADOXES. 

alike. The author of the Rambler^ is ridiculed, because his 
young ladies talk Johnsonese; but the satirists forget that 
all the presentable novel-writers were equally incompetent ; 
even the author of Zeluco (1789)4 is the strongest possible 
case in point. 

Dr. Moore,s the father of the hero of Corunna, 6 with 
good narrative power, some sly humor, and much observa- 
tion of character, would have been, in our day, a writer 
of the Peacock 7 family. Nevertheless, to one who is accus- 
tomed to our style of things, it is comic to read the dialogue 
of a jealous husband, a suspected wife, a faithless maid- 
servant, a tool of a nurse, a wrong-headed pomposity of a 
priest, and a sensible physician, all talking Dr. Moore 
through their masks. Certainly an Irish soldier does say 
"by Jasus," and a cockney footman "this here" and "that 
there" ; and this and the like is all the painting of characters 
which is effected out of the mouths of the bearers by a nar- 
rator of great power. I suspect that some novelists re- 
pressed their power under a rule that a narrative should nar- 
rate, and that the dramatic should be confined to the drama. 

I make no exception in favor of Miss Burney; 8 though 
she was the forerunner of a new era. Suppose a country 

8 That is, Dr. Johnson (1709-1784). The Rambler was published 
in 1750- 175 2 > and was an imitation of Addison's Spectator. 

4 Dr. Moore, referred to below. 

5 Dr. John Moore (1729-1802), physician and novelist, is now 
best known for his Journal during a Residence in France from the 
beginning of August to the middle of December, 1792, a work quoted 
frequently by Carlyle in his French Revolution. 

6 Sir John Moore (1761-1809), Lieutenant General in the Napo- 
leonic wars. He was killed in the battle of Corunna. The poem by 
Charles Wolfe (1791-1823), The Burial of Sir John Moore (1817), 
is well known. 

7 Referring to the novels of Thomas Love Peacock (1785-1866), 
who succeeded James Mill as chief examiner of the East India 
Company, and was in turn succeeded by John Stuart Mill. 

8 Frances Burney, Madame d'Arblay (1752-1840), married Gen- 
eral d'Arblay, a French officer and companion of Lafayette, in 1793- 
She was only twenty-five when she acquired fame by her Evelina, 
or a Young Lady's Entrance into the World. Her Letters and Diaries 
appeared posthumously (1842-45). 



A NEW ERA IN FICTION. 191 

in which dress is always of one color ; suppose an importer 
who brings in cargoes of blue stuff, red stuff, green stuff, 
etc., and exhibits dresses of these several colors, that person 
is the similitude of Miss Burney. It would be a delightful 
change from a universal dull brown, to see one person all 
red, another all blue, etc. ; but the real inventor of pleasant 
dress would be the one who could mix his colors and keep 
down the bright and gaudy. Miss Burney 's introduction 
was so charming, by contrast, that she nailed such men as 
Johnson, Burke, Garrick, etc., to her books. But when a 
person who has read them with keen pleasure in boyhood, as 
I did, comes back to them after a long period, during which 
he has made acquaintance with the great novelists of our 
century, three-quarters of the pleasure is replaced by wonder 
that he had not seen he was at a puppet-show, not at a drama. 
Take some labeled characters out of our humorists, let them 
be put together into one piece, to speak only as labeled : let 
there be a Dominie with nothing but "Prodigious !" a Dick 
Swiveller with nothing but adapted quotations; a Dr. Fol- 
liott with nothing but sneers at Lord Brougham ;9 and the 
whole will pack up into one of Miss Burney's novels. 

Maria Edgeworth, 10 Sydney Owenson (Lady Morgan), 11 
Jane Austen, 12 Walter Scott, 1 ^ etc., are all of our century ; as 

9 Henry Peter, Baron Brougham and Vaux (1778-1868), well 
known in politics, science, and letters. He was one of the founders 
of the Edinburgh Review, became Lord Chancellor in 1830, and took 
part with men like William Frend, De Morgan's father-in-law, in 
the establishing of London University. He was also one of the 
founders of the Society for the Diffusion of Useful Knowledge. He 
was always friendly to De Morgan, who entered the faculty of 
London University, whose work on geometry was published by the 
Society mentioned, and who was offered the degree of doctor of 
laws by the University of Edinburgh while Lord Brougham was 
Lord Rector. The Edinburgh honor was refused by De Morgan 
who said he "did not feel like an LL.D." 

10 Maria Edgeworth (1767-1849). 

11 Sydney Owenson (c. 1783-1859) married Sir Thomas Morgan, 
a well-known surgeon, in 1812. Her Irish stories were very popular 
with the patriots but were attacked by the Quarterly Review. The 
Wild Irish Girl (1806) went through seven editions in two years. 

18 1775-1817. 13 1771-1832. 



192 A BUDGET OF PARADOXES. 

are, I believe, all the Minerva Press novels, as they were 
called, which show some of the power in question. Perhaps 
dramatic talent found its best encouragement in the drama 
itself. But I cannot ascertain that any such power was di- 
rected at the multitude, whether educated or uneducated, 
with natural mixture of character, under the restraints of 
decorum, until the use of it by two religious writers of the 
school called "evangelical," Hannah More and Rowland 
Hill. 14 The Village Dialogues, though not equal to the Re- 
pository Tracts, are in many parts an approach, and perhaps 
a copy; there is frequently humorous satire, in that most 
effective form, self-display. They were published in 1800, 
and, partly at least, by the Religious Tract Society, the 
lineal successsor of the Repository association, though know- 
ing nothing about its predecessor. I think it right to add 
that Rowland Hill here mentioned is not the regenerator 
of the Post Office. 1 * Some do not distinguish accurately; 
I have heard of more than one who took me to have had 
a logical controversy with a diplomatist who died some 
years before I was born. 

THE RELIGIOUS TRACT SOCIETY. 

A few years ago, an attempt was made by myself and 
others to collect some information about the Cheap Reposi- 
tory (see Notes and Queries, 3d Series, vi. 241, 290, 353; 
Christian Observer, Dec. 1864, pp. 944-49). It appeared 
that after the Religious Tract Society had existed more than 
fifty years, a friend presented it with a copy of the original 
prospectus of the Repository, a thing the existence of which 
was not known. In this prospectus it is announced that 
from the plan "will be carefully excluded whatever is en- 
thusiastic, absurd, or superstitious." The "evangelical" 

"The famous preacher (1732-1808). He was the first chairman 
of the Religious Tract Society. He is also known as one of the 
earliest advocates of vaccination, in his Cow-pock Inoculation vindi- 
cated and recommended from matters of fact, 1806. 

15 Sir Rowland Hill (1795-1879), the father of penny postage. 



THE RELIGIOUS TRACT SOCIETY. 193 

party had, from the foundation of the Religious Tract So- 
ciety, regretted that the Repository Tracts "did not contain 
a fuller statement of the great evangelical principles" ; while 
in the prospectus it is also stated that "no cause of any par- 
ticular party is intended to be served by it, but general 
Christianity will be promoted upon practical principles." 
This explains what has often been noticed, that the tracts 
contain a mild form of "evangelical" doctrine, free from 
that more fervid dogmatism which appears in the Village 
Dialogues', and such as H. More's friend, Bishop Porteus 1 
a great promoter of the scheme might approve. The 
Religious Tract Society (in 1863) republished some of H. 
More's tracts, with alterations, additions, and omissions ad 
libitum. This is an improper way of dealing with the works 
of the dead ; especially when the reprints are of popular 
works. A small type addition to the preface contains: 
"Some alterations and abridgements have been made to 
adapt them to the present times and the aim of the Religious 
Tract Society." I think every publicity ought to be given 
to the existence of such a practice ; and I reprint what I 
said on the subject in Notes and Queries. 

Alterations in works which the Society fepublishes are 
a necessary part of their plan, though such notes as they 
should judge to be corrective would be the best way of pro- 
ceeding. But the fact of alteration should be very distinctly 
announced on the title of the work itself, not left to a little 
bit of small type at the end of the preface, in the place 
where trade advertisements, or directions to the binder, are 
often found. And the places in which alteration has been 
made should be pointed out, either by marks of omission, 
when omission is the alteration, or by putting the altered 
sentences in brackets, when change has been made. May 
any one alter the works of the dead at his own discretion? 



ilby Porteus (1731-1808), Bishop of Chester (1776) and 
Bishop of London (1787). He encouraged the Sunday-school move- 
ment and the dissemination of Hannah More's tracts. He was an 
active opponent of slavery, but also of Catholic emancipation. 



194 A BUDGET OF PARADOXES. 

We all know that readers in general will take each sentence 
to be that of the author whose name is on the title ; so that 
a correcting republisher makes use of his author s name to 
teach his own variation. The tortuous logic of "the trade," 
which is content when "the world" is satisfied, is not easily 
answered, any more than an eel is easily caught; but the 
Religious Tract Society may be convinced [in the old sense] 
in a sentence. On which course would they feel most safe 
in giving their account to the God of truth? "In your own 
conscience, now?" 

1 have tracked out a good many of the variations made 
by the Religious Tract Society in the recently published 
volume of Repository Tracts. Most of them are doctrinal 
insertions or amplifications, to the matter of which Hannah 
More would not have objected all that can be brought 
against them is the want of notice. But I have found two 
which the respect I have for the Religious Tract Society, 
in spite of much difference on various points, must not 
prevent my designating as paltry. In the story of Mary 
Wood, a kind-hearted clergyman converses with the poor 
girl who has ruined herself by lying. In the original, he 
"assisted her in the great work of repentance ;" in the re- 
print it is to be shown in some detail how he did this. He 
is to begin by pointing out that "the heart is deceitful above 
all things and desperately wicked." Now the clergyman's 
name is Heart-well: so to prevent his name from contra- 
dicting his doctrine, he is actually cut down to Harwell. 
Hannah Moore meant this good man for one of those de- 
scribed in Acts xv. 8, 9, and his name was appropriate. 

Again, Mr. Flatterwell, in persuasion of Parley the porter 
to let him into the castle, declares that the worst he will do 
is to "play an innocent game of cards just to keep you awake, 
or sing a cheerful song w r ith the maids." Oh fie! Miss 
Hannah More ! and you a single lady too, and a contempo- 
rary of the virtuous Bowdler! 2 Though Flatterwell be an 

2 Henrietta Maria Bowdler (1754-1830), generally known as Mrs. 



THE RELIGIOUS TRACT SOCIETY. 195 

allegory of the devil, this is really too indecorous, even for 
him. Out with the three last words! and out it is. 

The Society cuts a poor figure before a literary tribunal. 
Nothing was wanted except an admission that the remarks 
made by me were unanswerable, and this was immediately 
furnished by the Secretary (N. and Q. } 3d S., vi. 290). In 
a reply of which six parts out of seven are a very amplified 
statement that the Society did not intend to reprint all Han- 
nah More's tracts, the remaining seventh is as follows: 

"I am not careful [perhaps this should be careful not} to 
notice Professor De Morgan's objections to the changes in 
'Mary Wood' or 'Parley the Porter,' but would merely re- 
iterate that the tracts were neither designed nor announced 
to be 'reprints' of the originals [design is only known to 
the designers ; as to announcement, the title is ' 'Tis all for 
the best, The Shepherd of Salisbury Plain, and other narra- 
tives by Hannah More'] ; and much less [this must be care- 
ful not\ further removed from answer than not careful} 
can I occupy your space by a treatise on the Professor's ques- 
tion : 'May any one alter the works of the dead at his own 
discretion ?' " 
To which I say: Thanks for help! 

I predict that Hannah More's Cheap Repository Tracts 
will somewhat resemble the Pilgrim's Progress in their fate. 
Written for the cottage, and long remaining in their original 
position, they will become classical works of their kind. 
Most assuredly this will happen if my assertion cannot be 
upset, namely, that they contain the first specimens of fiction 
addressed to the world at large, and widely circulated, in 
which dramatic as distinguished from puppet power is 
shown, and without indecorum. 

Harriet Bowdler. She was the author of many religious tracts and 
poems. Her Poems and Essays (1786) were often reprinted. The 
story goes that on the appearance of her Sermons on the Doctrines 
and Duties of Christianity (published anonymously), Bishop Por- 
teus offered the author a living under the impression that it was 
written by a man. 



196 A BUDGET OF PARADOXES. 

t 

According to some statements I have seen, but which 
I have riot verified, other publishing bodies, such as the 
Christian Knowledge Society, have taken the same liberty 
with the names of the dead as the Religious Tract Society. 3 
If it be so, the impropriety is the work of the smaller spirits 
who have not been sufficiently overlooked. There must be 
an overwhelming majority in the higher councils to feel 
that, whenever altered works are published, the fact of 
alteration should be made as prominent as the 'name of the 
author. Everything short of this is suppression of truth, 
and will ultimately destroy the credit of the Society. Equally 
necessary is it that the alterations should be noted. When it 
comes to be known that the author before him is altered, 
he knows not where nor how nor by whom, the lowest 
reader will lose his interest. 

A TRIBUTE TO WILLIAM FREND. 

The principles of Algebra. By William Frend. 1 London, 1796, 
8vo. Second Part, 1799. 

This Algebra, says Dr. Peacock, 2 shows "great distrust 

1 William Frend (1757-1841), whose daughter Sophia Elizabeth 
became De Morgan's wife (1837), was at one time a clergyman of 
the Established Church, but was converted to Unitarianism (1787). 
He came under De Morgan's definition of a true paradoxer, carry- 
ing on a zealous warfare for what he thought right. As a result 
of his Address to the Inhabitants of Cambridge (1787), and his 
efforts to have abrogated the requirement that candidates for the 
M.A. must subscribe to the thirty-nine articles, he was deprived of 
his tutorship in 1788. A little later he was banished (see De Mor- 
gan's statement in the text) from Cambridge because of his denun- 
ciation of the abuses of the Church and his condemnation of the 
liturgy. His eccentricity is seen in his declining to use negative 
quantities in the operations of algebra. He finally became an actuary 
at London and was prominent in radical associations. He was a 
mathematician of ability, having been second wrangler and having 
nearly attained the first place, and he was also an excellent scholar 
in Latin, Greek, and Hebrew. 

'George Peacock (1791-1858), Fellow of Trinity College, Cam- 
bridge, Lowndean professor of astronomy, and Dean of Ely Cathe- 
dral (1839). His tomb may be seen at Ely where he spent the latter 
part of his life. He was one of the group that introduced the mod- 
ern continental notation of the calculus into England, replacing 



A TRIBUTE TO WILLIAM FREND. 197 

of the results of algebraical science which were in existence 
at the time when it was written/' Truly it does ; for, as 
Dr. Peacock had shown by full citation, it makes war of 
extermination upon all that distinguishes algebra from arith- 
metic. Robert Simson 3 and Baron Maseres 4 were Mr. Frend's 
predecessors in this opinion. 

The genuine respect which I entertained for my father- 
in-law did not prevent my canvassing with perfect freedom 
his anti-algebraical and anti-Newtonian opinions, in a long 
obituary memoir read at the Astronomical Society in Feb- 
ruary 1842, which was written by me. It was copied into 
the Athen&um of March 19. It must be said that if the 
manner in which algebra was presented to the learner had 
been true algebra, he would have been right : and if he had 
confined himself to protesting against the imposition of at- 
traction as a fundamental part of the existence of matter, 
he would have been in unity with a great many, including 
Newton himself. I wish he had preferred amendment to 
rejection when he was a college tutor: he wrote and spoke 
English with a clearness which is seldom equaled. 

His anti-Newtonian discussions are confined to the pre- 
liminary chapters of his Evening Amusements, 5 a series of 
astronomical lessons in nineteen volumes, following the 
moon through a period of the golden numbers. 

There is a mistake about him which can never be de- 
stroyed. It is constantly said that, at his celebrated trial in 
1792, for sedition and opposition to the Liturgy, etc., he was 
expelled from the University. He was banished. People 
cannot see the difference; but it made all the difference to 

the cumbersome notation of Newton, passing from "the dofage 
of fluxions to the deism of the calculus." 

'Robert Simson (1687-1768), professor of mathematics at Glas- 
gow. His restoration of Apollonius (1749) and his translation and 
restoration of Euclid (1756, and 1776 posthumous) are well known. 

4 Francis Maseres (1731-1824), a prominent lawyer. His mathe- 
matical works had some merit. 

5 These appeared annually from 1804 to 1822. 



198 A BUDGET OF PARADOXES. 

Mr. Frend. He held his fellowship and its profits till his 
marriage in 1808, and was a member of the University and 
of its Senate till his death in 1841, as any Cambridge Calen- 
dar up to 1841 will show. That they would have expelled 
him if they could, is perfectly true; and there is a funny 
story also perfectly true about their first proceedings be- 
ing under a statute which would have given the power, had 
it not been discovered during the proceedings that the statute 
did not exist. It had come so near to existence as to be en- 
tered into the Vice-Chancellor's book for his signature, 
which it wanted, as was not seen till Mr. Frend exposed it: 
in fact, the statute had never actually passed. 

There is an absurd mistake in Gunning's 6 Reminiscences 
of Cambridge. In quoting a passage of Mr. Frend's pam- 
phlet, which was very obnoxious to the existing Government, 
it is printed that the poor market-women complained that 
they were to be scotched a quarter of their wages by taxation ; 
and attention is called to the word by its being three times 
printed in italics. In the pamphlet it is "sconced" ; that 
very common old word for fined or mulcted. 

Lord Lyndhurst, 7 who has [1863] just passed away under 
a load of years and honors, was Mr. Frend's private pupil 
at Cambridge. At the time of the celebrated trial, he and 
two others amused themselves, and vented the feeling which 
was very strong among the undergraduates, by chalking the 
walls of Cambridge with "Frend for ever!" While thus 
engaged in what, using the term legally, we are probably 
to call his first publication, he and his friends were surprised 
by the proctors. Flight and chase followed of course : Cop- 
ley and- one of the others, Serjeant Rough, 8 escaped ; the 

"Henry Gunning (1768-1854) was senior esquire bedell of Cam- 
bridge. The Reminiscences appeared in two volumes in 1854. 

7 John Singleton Copley, Baron Lyndhurst (1772-1863), the 
son of John Singleton Copley the portrait painter, was born in Bos- 
ton. He was educated at Trinity College, Cambridge, and became a 
lawyer. He was made Lord Chancellor in 1827. 

'Sir William Rough (c. 1772-1838), a lawyer and poet, became 
Chief Justice of Ceylon in 1836. He was knighted in 1837. 



A TRIBUTE TO WILLIAM FREND. 199 

third, whose name I forget, but who afterwards, I have been 
told was a bishop, 9 being lame, was captured and imposi- 
tioned. Looking at the Cambridge Calendar to verify the 
fact that Copley was an undergraduate at the time, I find 
that there are but two other men in the list of honors 
of his year whose names are now widely remembered. And 
they were both celebrated schoolmasters; Butler 10 of Har- 
row, and Tate 11 of Richmond. 

But Mr. Frend had another noted pupil. I once had a 
conversation with a very remarkable man, who was gen- 
erally called "Place, 12 the tailor," but who was politician, 
political economist, etc., etc. He sat in the room above his 
shop he was then a thriving master tailor at Charing Cross 
surrounded by books enough for nine, to shame a proverb. 
The blue books alone, cut up into strips, would have measured 
Great Britain for oh-no-we-never-mention-'ems, the High- 
lands included. I cannot find a biography of this worthy 
and able man. I happened to mention William Frend, and 
he said, "Ah! my old master, as I always call him. Many 
and many a time, and year after year, did he come in every 

"Herbert Marsh, afterwards Bishop of Peterborough, a relation 
of my father. S. E. De M. 

He was born in 1757 and died in 1839. On the trial of Frend 
he publicly protested against testifying against a personal confidant, 
and was excused. He was one of the first of the English clergy to 
study modern higher criticism of the Bible, and amid much opposi- 
tion he wrote numerous works on the subject. He was professor of 
theology at Cambridge (1707), Bishop of Llandaff (1816), and 
Bishop of Peterborough. 

10 George Butler (1774-1853), Headmaster of Harrow (1805- 
1829), Chancellor of Peterborough (1836), and Dean of Peterbor- 
ough (1842). 

"James Tate (1771-1843), Headmaster of Richmond School 
(1796-1833) and Canon of St. Paul's Cathedral (1833). He left 
several works on the classics. 

"Francis Place (1771-1854), at first a journeyman breeches 
maker, and later a master tailor. He was a hundred years ahead of 
his time as a strike leader, but was not so successful as an agitator 
as he was as a tailor, since his shop in Charing Cross made him 
wealthy. He was a well-known radical, and it was largely due to 
his efforts that the law against the combinations of workmen was 
repealed in 1824. His chief work was The Principles of Population 
(1822). 



200 A BUDGET OF PARADOXES. 

now and then to give me instruction, while I was sitting 
on the board, working for my living, you know." 

Place, who really was a sound economist, is joined with 
Cobbett, because they were together at one time, and because 
he was, in 1800, etc., a great Radical. But for Cobbett he 
had a great contempt. He told me the following story. He 
and others were advising with Cobbett about the defense 
he was to make on a trial for seditious libel which was com- 
ing on. Said Place, "You must put in the letters you have 
received from Ministers, members of the Commons from the 
Speaker downwards, etc., about your Register, and their 
wish to have subjects noted. You must then ask the jury 
whether a person so addressed must be considered as a com- 
mon sower of sedition, etc. You will be acquitted ; nay, if 
your intention should get about, very likely they will man- 
age to stop proceedings." Cobbett was too much disturbed 

to listen ; he walked about the room ejaculating "D the 

prison !" and the like. He had not the sense to follow the 
advice, and was convicted. 

Cobbett, to go on with the chain, was a political acrobat, 
ready for any kind of posture. A friend of mine gave me 
several times an account of a mission to him. A Tory mem- 
ber those who know the old Tory world may look for his 
initials in initials of two consecutive words of "Pay his 
money with interest" who was, of course, a political oppo- 
nent, thought Cobbett had been hardly used, and deter- 
mined to subscribe handsomely towards the expenses he was 
incurring as a candidate. My friend was commissioned to 
hand over the money a bag of sovereigns, that notes might 
not be traced. He went into Cobbett's committee-room, 
told the patriot his errand, and put the money on the table. 
"And to whom, sir, am I indebted?" said Cobbett. "The 
donor," was the answer, "is Mr. Andrew Theophilus Smith," 
or some such unlikely pair of baptismals. "Ah !" said Cob- 
bett, "I have known Mr. A. T. S. a long time ! he was always 
a true friend of his country !" 



A TRIBUTE TO WILLIAM FREND. 201 

To return to Place. He is a noted instance of the ad- 
vantage of our jury system, which never asks a man's poli- 
tics, etc. The late King of Hanover, when Duke of Cumber- 
land, being unpopular, was brought under unjust suspicions 
by the suicide of his valet: he must have seduced the wife 
and murdered the husband. The charges were as absurd 
as those brought against the Englishman in the Frenchman's 
attempt at satirical verses upon him: 

"The Englishman is a very bad man; 
He drink the beer and he steal the can : 
He kiss the wife and he beat the man ; 
And the Englishman is a very G d ." 

The charges were revived in a much later day, and the 
defense might have given some trouble. But Place, who 
had been the foreman at the inquest, came forward, and 
settled the question in a few lines. Every one knew that 
the old Radical was quite free of all disposition to suppress 
truth from wish to curry favor with royalty. 

John Speed, 13 the author of the English History, 14 1632) 
which Bishop Nicolson 15 calls the best chronicle extant, was 
a man, like Place, of no education, but what he gave himself. 
The bishop says he would have done better if he had a better 
training: but what, he adds, could have been expected from 
a tailor! This Speed was, as well as Place. But he was 

"Speed (1552-1629) was a tailor until Grevil (Greville) made 
him independent of his trade. He was not only an historian of 
some merit, but a skilful cartographer. His maps of the counties 
were collected in the Theatre of the Empire of Great Britaine, 1611. 
About this same time he also published Genealogies recorded in 
Sacred Scripture, a work that had passed through thirty-two edi- 
tions by 1640. 

14 The history of Great Britaine under the conquests of ye Ro- 
mans, Saxons, Danes, and Normans London, 1611, folio. The 

second edition appeared in 1623 ; the third, to which De Morgan here 
refers, posthumously in 1632; and the fourth in 1650. 

"William Nicolson (1655-1727) became Bishop of Carlisle in 
1702, and Bishop of Derry in 1718, His chief work was the Histor- 
ical Library (1696-1724), in the form of a collection of documents 
and chronicles. It was reprinted in 1736 and in 1776. 



202 A BUDGET OF PARADOXES. 

released from manual labor by Sir Fulk Grevil, 16 who en- 
abled him to study. 

A STORY ON SIMSON. 

I have elsewhere noticed that those who oppose the mys- 
teries of algebra do not ridicule them; this I want the cy- 
clometers to do. Of the three who wrote against the great 
point, the negative quantity, and the uses of which are 
connected with it, only one could fire a squib. That Robert 
Simson 1 should do such a thing will be judged impossible 
by all who admit tradition. I do not vouch for the follow- 
ing; I give it as a proof of the impression which prevailed 
about him: 

He used to sit at his open window on the ground floor, 
as deep in geometry as a Robert Simson ought to be. Here 
he would be accosted by beggars, to whom he generally 
gave a trifle, he roused himself to hear a few words of the 
story, made his donation, and instantly dropped down into 
his depths. Some wags one day stopped a mendicant who 
was on his way to the window with "Now, my man, do as 
we tell you, and you will get something from that gentle- 
man, and a shilling from us besides. You will go and say 
you are in distress, he will ask you who you are, and you 
will say you are Robert Simson, son of John Simson of 
Kirktonhill." The man did as he was told ; Simson quietly 
gave him a coin, and dropped off. The wags watched a 
little, and saw him rouse himself again, and exclaim "Robert 
Simson, son of John Simson of Kirktonhill ! why, that is my- 
self. That man must be an impostor." Lord Brougham 
tells the same story, with some difference of details. 

"Sir Fulk Grevil, or Fulke Greville (1554-1628), was a favorite 
of Queen Elizabeth, Chancellor of the Exchequer under James I, a 
patron of literature, and a friend of Sir Philip Sidney. 

1 See note 4 on page 197. 



BARON MASERES. 203 



BARON MASERES. 

Baron Maseres 1 was, as a writer, dry ; those who knew 
his writings will feel that he seldom could have taken in a 
joke or issued a pun. Maseres was the fourth wrangler 
of 1752, and first Chancellor's medallist (or highest in clas- 
sics) ; his second was Porteus 2 (afterward Bishop of Lon- 
don). Waring3 came five years after him: he could not 
get Maseres through the second page of his first book on 
algebra ; a negative quantity stood like a lion in the way. 
In 1758 he published his Dissertation on the Use of the 
Negative Sign* 4to. There are some who care little about 
+ and , who would give it house-room for the sake of 
the four words "Printed by Samuel Richardson." 

Maseres speaks as follows : "A single quantity can never 
be marked with either of those signs, or considered as 
either affirmative or negative ; for if any single quantity, as 
b, is marked either with the sign -|- or with the sign 
without assigning some other quantity, as a, to which it is 
to be added, or from which it is to be subtracted, the mark 
will have no meaning or signification: thus if it be said 
that the square of 5, or the product of 5 into 5, is 
equal to +25, such an assertion must either signify no more 
than that 5 times 5 is equal to 25 without any regard to the 
signs, or it must be mere nonsense and unintelligible jargon. 
I speak according to the foregoing definition, by which the 
affirmativeness or negativeness of any quantity implies a 
relation to another quantity of the same kind to which it 

1 See note 5 on page 197. 

2 See note on page 193. 

8 Edward Waring (1736-1796) was Lucasian professor of mathe- 
matics at Cambridge. He published several works on analysis and 
curves. The work referred to was the Miscellanea Analytic? de 
aequationibus algebraicis et curvarum proprietatibus, Cambridge, 
1762. 

* A Dissertation on the use of the Negative Sign in Algebra ; 

to which is added, Machin's Quadrature of the Circle, London, 1758. 



204 A BUDGET OF PARADOXES. 

is added, or from which it is subtracted ; for it may perhaps 
be very clear and intelligible to those who have formed to 
themselves some other idea of affirmative and negative quan- 
tities different from that above denned." 

Nothing can be more correct, or more identically logical : 
+5 and 5, standing alone, are jargon if +5 and 5 are 
to be understood as without reference to another quantity. 
But those who have "formed to themselves some other idea" 
see meaning enough. The great difficulty of the opponents 
of algebra lay in want of power or will to see extension of 
terms. Maseres is right when he implies that extension, 
accompanied by its refusal, makes jargon. One of my para- 
doxers was present at a meeting of the Royal Society (in 
1864, I think) and asked permission to make some remarks 
upon a paper. He rambled into other things, and, naming 
me, said that I had written a book in which two sides of a 
triangle are pronounced equal to the third. s So they are, 
in the sense in which the word is used in complete algebra ; 
in which A+B = C makes A, B, C, three sides of a triangle, 
and declares that going over A and B, one after the other, 
is equivalent, in change of place, to going over C at once. 
My critic, who might, if he pleased, have objected to exten- 
sion, insisted upon reading me in unextended meaning. 

On the other hand, it must be said that those who wrote 
on the other idea wrote very obscurely about it and justified 
Des Cartes (De Methodo) 6 when he said: "Algebram vero, 
ut solet doceri, animadvert! certis regulis et numerandi for- 
mulis ita esse contentam, ut videatur potius ars quaedam 
confusa, cujus usu ingenium quodam modo turbatur et ob- 
scuratur, quam scientia qua excolatur et perspicacius redda- 

B The paper was probably one on complex numbers, or possibly 
one on quaternions, in which direction as well as absolute value is 
involved. 

8 De Morgan quotes from one of the Latin editions. Descartes 
wrote in French, the title of his first edition being: Discours de la 
methode pour bien conduire sa raison et chercher la verite dans les 
sciences, plus la dioptrique, les meteores et la geometrie qui sont des 
essais de cette methode, Leyden, 1637, 4to. 



BARON MASERES. 205 

tur."7 Maseres wrote this sentence on the title of his own 
work, now before me ; he would have made it his motto if 
he had found it earlier. 

There is, I believe, in Cobbett's Annual Register? an ac- 
count of an interview between Maseres and Cobbett when 
in prison. 

The conversation of Maseres was lively, and full of se- 
rious anecdote: but only one attempt at humorous satire is 
recorded of him; it is an instructive one. He was born in 
1731 (Dec. 15), and his father was a refugee. French was 
the language of the house, with the pronunciation of the 
time of Louis XIV. He lived until 1824 (May 19), and saw 
the race of refugees who were driven out by the first Revo- 
lution. Their pronunciation differed greatly from his own ; 
and he used to amuse himself by mimicking them. Those 
who heard him and them had the two schools of pronuncia- 
tion before them at once ; a thing which seldom happens. 
It might even yet be worth while to examine the Canadian 
pronunciation. 

Maseres went as Attorney-General to Quebec; and was 
appointed Cursitor Baron of our Exchequer in 1773. There 
is a curious story about his mission to Canada, which I have 
heard as good tradition, but have never seen in print. The 
reader shall have it as cheap as I ; and I confess I rather 
believe it. Maseres was inveterately honest ; he could not, 
at the bar, bear to see his own client victorious, when he 
knew his cause was a bad one. On a certain occasion he 
was in a cause which he knew would go against him if a 
certain case were quoted. Neither the judge nor the oppo- 
site counsel seemed to remember this case, and Maseres 
could not help dropping an allusion which brought it out. 

T "I have observed that algebra indeed, as it is usually taught, 
is so restricted by definite rules and formulas of calculation, that it 
seems rather a confused kind of an art, by the practice of which 
the mind is in a certain manner disturbed and obscured, than a 
science by which it is cultivated and made acute." 

"It appeared in 93 volumes, from 1758 to 1851. 



206 A BUDGET OF PARADOXES. 

His business as a barrister fell off, of course. Some time 
after, Mr. Pitt (Chatham) wanted a lawyer to send to Can- 
ada on a private mission, and wanted a very honest man. 
Some one mentioned Maseres, and told the above story: 
Pitt saw that he had got the man he wanted. The mission 
was satisfactorily performed, and Maseres remained as At- 
torney-General. 

The Doctrine of Life Annuities 9 (4to, 726 pages, 1783) 
is a strange paradox. Its size, the heavy dissertations on 
the national debt, and the depth of algebra supposed known, 
put it out of the question as an elementary work, and it is 
unfitted for the higher student by its elaborate attempt at 
elementary character, shown in its rejection of forms derived 
from chances in favor of the average, and its exhibition of 
the separate values of the years of an annuity, as arithmetical 
illustrations. It is a climax of unsaleability, unreadability, 
and inutility. For intrinsic nullity of interest, and dilution 
of little matter with much ink, I can compare this book to 
nothing but that of Claude de St. Martin, elsewhere men- 
tioned, or the lectures On the Nature and Properties of Log- 
arithms, by James Little, 10 Dublin, 1830, 8vo. (254 heavy 
pages of many words and few symbols), a wonderful weight 
of weariness. 

The stock of this work on annuities, very little dimin- 
ished, was given by the author to William Frend, who paid 
warehouse room for it until about 1835, when he consulted 
me as to its disposal. As no publisher could be found who 
would take it as a gift, for any purpose of sale, it was con- 
signed, all but a few copies, to a buyer of waste paper. 

Baron Maseres's republications are well known: the 
Scriptores Logarithmici 11 is a set of valuable reprints, mixed 

9 The principles of the doctrine of life -annuities; explained in 

a familiar manner with a variety of new tables ...., London, 

1783. 

10 1 suppose the one who wrote Conjectures on the physical causes 
of Earthquakes and Volcanoes, Dublin, 1820. 

11 Scriptores Logarithmici; or, a Collection of several curious 






BARON MASERES. 207 

with much which might better have entered into another 
collection. It is not so well known that there is a volume 
of optical reprints, Script ores Optici, London, 1823, 4to, 
edited for the veteran of ninety-two by Mr. Babbage 12 at 
twenty-nine. This excellent volume contains James Greg- 
ory, Des Cartes, Halley, Barrow, and the optical writings 
of Huyghens, the Principia of the undulatory theory. It 
also contains, by the sort of whim in which such men as 
Maseres, myself, and some others are apt to indulge, a reprint 
of "The great new Art of weighing Vanity," 1 ^ by M. Patrick 
Mathers, Arch-Bedel to the University of St. Andrews, 
Glasgow, 1672. Professor Sinclair, T * of Glasgow, a good man 
at clearing mines of the water which they did not want, and 
furnishing cities with water which they did want, seems to 
have written absurdly about hydrostatics, and to have at- 
tacked a certain Sanders, 1 * M.A. So Sanders, assisted by 
James Gregory, published a heavy bit of jocosity about him. 
This story of the authorship rested on a note made in his 

tracts on the nature and construction of Logarithms.... together 
with same tracts on the Binomial Theorem...., 6 vols., London, 
1791-1807. 

"Charles Babbage (1792-1871), whose work on the calculating 
machine is well known. Maseres was, it is true, ninety-two at this 
time, but Babbage was thirty-one instead of twenty-nine. He had 
already translated Lacroix's Treatise on the differential and integral 
calculus (1816), in collaboration with Herschel and Peacock. He 
was Lucasian professor of mathematics at Cambridge from 1828 to 
1839- 

" The great and new Art of weighing Vanity, or a discovery of 
the ignorance of the great and new artist in his pseudo-philosophical 
writings. The "great and new artist" was Sinclair. 

"George Sinclair, probably a native of East Lothian, who died 
in 1696. He was professor of philosophy and mathematics at Glas- 
gow, and was one of the first to use the barometer in measuring 
altitudes. The work to which De Morgan refers is his Hydrostaticks 
(1672). He was a firm believer in evil spirits, his work on the 
subject going through four editions: Satan's Invisible World Dis- 
covered; or, a choice collection of modern relations, proving evi- 
dently against the Saducees and Athiests of this present age, that 
there are Devils, Spirits, Witches, and Apparitions, Edinburgh, 1685. 

16 This was probably William Sanders, Regent of St. Leonard's 
College, whose Theses philosophicae appeared in 1674, and whose 
Elementa geometriae came out a dozen years later. 



208 A BUDGET OF PARADOXES. 

copy by Robert Gray, M.D. ; but it has since been fully con- 
firmed by a letter of James Gregory to Collins, in the 
Macclesfield Correspondence. "There is one Master Sin- 
clair, who did write the Ars Magna et Nova, 16 a pitiful ig- 
norant fellow, who hath lately written horrid nonsense in 
the hydrostatics, and hath abused a master in the University, 
one Mr. Sanders, in print. This Mr. Sanders .... is resolved 
to cause the Bedel of the University to write against him . . . 
We resolve to make excellent sport with him." 

On this I make two remarks : First, I have learned from 
experience that old notes, made in books by their possessors, 
are statements of high authority: they are almost always 
confirmed. I do not receive them without hesitation ; but I 
believe that of all the statements about books which rest on 
one authority, there is a larger percentage of truth in the 
written word than in the printed word. Secondly, I mourn 
to think that when the New Zealander picks up his old copy 
of this book, and reads it by the associations of his own day, 
he may, in spite of the many assurances I have received that 
my Athen&um Bridget was amusing, feel me to be as heavy 
as I feel James Gregory and Sanders. But he will see that 
I knew what was coming, which Gregory did not. 

MR. TREND'S BURLESQUE. 

It was left for Mr. Frend to prove that an impugner of 
algebra could attempt ridicule. He was, in 1803, editor of 
a periodical The Gentleman's Monthly Miscellany, which 
lasted a few months. 1 To this, among other things, he con- 
tributed the following, in burlesque of the use made of 0, 
to which he objected. 2 The imitation of Rabelais, a writer 

18 Ars nova et magna gravitatis et levitatis^. sive dialogorum phi- 
losophicorum libri sex de aeris vera ac reali gravitate, Rotterdam, 
1669, 4to. 

1 Volume I, Nos. I and 2, appeared in 1803. 

3 His daughter, Mrs. De Morgan, says in her Memoir of her 
husband: "My father had been second wrangler in a year in which 
the two highest were close together, and was, as his son-in-law 
afterwards described him, an exceedingly clear thinker. It is pos- 



MR. TREND'S BURLESQUE. 209 

in whom he delighted, is good: to those who have never 
dipped, it may give such a notion as they would not easily 
get elsewhere. The point of the satire is not so good. But 
in truth it is not easy to make pungent scoffs upon what is 
common sense to all mankind. Who can laugh with effect 
at six times nothing is nothing, as false or unintelligible? 
In an article intended for that undistinguishing know-0 the 
"general reader," there would have been no force of satire, 
if division by had been separated from multiplication by 
the same. 

I have followed the above by another squib, by the same 
author, on the English language. The satire is covertly 
aimed at theological phraseology ; and any one who watches 
this subject will see that it is a very just observation that 
the Greek words are not boiled enough. 

PANTAGRUEI/S DECISION of the QUESTION about NOTHING. 

"Pantagruel determined to have a snug afternoon with 
Epistemon and Panurge. Dinner was ordered to be set in 
a small parlor, and a particular batch of Hermitage with 
some choice Burgundy to be drawn from a remote corner 
of the cellar upon the occasion. By way of lunch, about 
an hour before dinner, Pantagruel was composing his stom- 
ach with German sausages, reindeer's tongues, oysters, 
brawn, and half a dozen different sorts of English beer 
just come into fashion, when a most thundering knocking 
was heard at the great gate, and from the noise they ex- 
pected it to announce the arrival at least of the First Consul, 
or king Gargantua. Panurge was sent to reconnoiter, and 
after a quarter of an hour's absence, returned with the 
news that the University of Pontemaca was waiting his high- 
ness's leisure in the great hall, to propound a question which 

sible, as Mr. De Morgan said, that this mental clearness and direct- 
ness may have caused his mathematical heresy, the rejection of the 
use of negative quantities in algebraical operations; and it is prob- 
able that he thus deprived himself of an instrument of work, the use 
of which might have led him to greater eminence in the higher 
branches." Memoir of Augustus De Morgan, London, 1882, p. 19. 



210 A BUDGET OF PARADOXES. 

had turned the brains of thirty-nine students, and had flung 
twenty-seven more into a high fever. With all my heart, 
says Pantagruel, and swallowed down three quarts of Bur- 
ton ale ; but remember, it wants but an hour of dinner time, 
and the question must be asked in as few words as possible ; 
for I cannot deprive myself of the pleasure I expected to 
enjoy in the company of my good friends for a set of mad- 
headed masters. I wish brother John was here to settle 
these matters with the black gentry. 

"Having said or rather growled this, he proceeded to the 
hall of ceremony, and mounted his throne; Epistemon and 
Panurge standing on each side, but two steps below him. 
Then advanced to the throne the three beadles of the Uni- 
versity of Pontemaca with their silver staves on their shoul- 
ders, and velvet caps on their heads, and they were followed 
by three times three doctors, and thrice three times three 
masters of art ; for everything was done in Pontemaca by the 
number three, and on this account the address was written 
on parchment, one foot in breadth, and thrice three times 
thrice three feet in length. The beadles struck the ground 
with their heads and their staves three times in approaching 
the throne ; the doctors struck the ground with their heads 
thrice three times, and the masters did the same thrice each 
time, beating the ground with their heads thrice three times. 
This was the accustomed form of approaching the throne, 
time out of mind, and it was said to be emblematic of the 
usual prostration of science to the throne of greatness. 

"The mathematical professor, after having spit, and 
hawked, and cleared his throat, and blown his nose on a 
handkerchief lent to him, for he had forgotten to bring his 
own, began to read the address. In this he was assisted by 
three masters of arts, one of whom, with a silver pen, 
pointed out the stops ; the second with a small stick rapped 
his knuckles when he was to raise or lower his voice; and 
a third pulled his hair behind when he was to look Pan- 
tagruel in the face. Pantagruel began to chafe like a lion : 



MR. TREND'S BURLESQUE. 211 

he turned first on one side, then on the other: he listened 
and groaned, and groaned and listened, and was in the ut- 
most cogitabundity of cogitation. His countenance began 
to brighten, when, at the end of an hour, the reader stam- 
mered out these words : 

" 'It has therefore been most clearly proved that as all 
matter may be divided into parts infinitely smaller than the 
infinitely smallest part of the infinitesimal of nothing, so 
nothing has all the properties of something, and may be- 
come, by just and lawful right, susceptible of addition, sub- 
traction, multiplication, division, squaring, and cubing: that 
it is to all intents and purposes as good as anything that 
has been, is, or can be taught in the nine universities of the 
land, and to deprive it of its rights is a most cruel innova- 
tion and usurpation, tending to destroy all just subordina- 
tion in the world, making all universities superfluous, level- 
ing vice-chancellors, doctors, and proctors, masters, bach- 
elors, and scholars, to the mean and contemptible state of 
butchers and tallow-chandlers, bricklayers and chimney- 
sweepers, who, if it were not for these learned mysteries, 
might think that they knew as much as their betters. Every 
one then, who has the good of science at heart, must pray 
for the interference of his highness to put a stop to all the 
disputes about nothing, and by his decision to convince all 
gainsayers that the science of nothing is taught in the best 
manner in the universities, to the great edification and im- 
provement of all the youth in the land/ 

"Here Pantagruel whispered in the ear of Panurge, who 
nodded to Epistemon, and they two left the assembly, and 
did not return for an hour, till the orator had finished his 
task. The three beadles had thrice struck the ground with 
their heads and staves, the docters had finished their com- 
pliments, and the masters were making their twenty-seven 
prostrations. Epistemon and Panurge went up to Panta- 
gruel, whom they found fast asleep and snoring ; nor could 
he be roused but by as many tugs as there had been bow- 



212 A BUDGET OF PARADOXES. 

ings from the corps of learning. At last he opened his 
eyes, gave a good stretch, made half a dozen yawns, and 
called for a stoup of wine. I thank you, my masters, says 
he; so sound a nap I have not had since I came from the 
island of Priestfolly. Have you dined, my masters? They 
answered the question by as many bows as at entrance ; but 
his highness left them to the care of Panurge, and retired 
to the little parlor with Epistemon, where they burst into 
a fit of laughter, declaring that this learned Baragouin about 
nothing was just as intelligible as the lawyer's Galimathias. 
Panurge conducted the learned body into a large saloon, 
and each in his way hearing a clattering of plates and glasses, 
congratulated himself on his approaching good cheer. There 
they were left by Panurge, who took his chair by Pantagruel 
just as the soup was removed, but he made up for the want 
of that part of his dinner by a pint of champagne. The 
learning of the university had whetted their appetites ; what 
they each ate it is needless to recite ; good wine, good stories, 
and hearty laughs went round, and three hours elapsed be- 
fore one soul of them recollected the hungry students of 
Pontemaca. 

"Epistemon reminded them of the business in hand, and 
orders were given for a fresh dozen of hermitage to be put 
upon table, and the royal attendants to get ready. As soon 
as the dozen bottles were emptied, Pantagruel rose from 
table, the royal trumpets sounded, and he was accompanied 
by the great officers of his court into the large dining hall, 
where was a table with forty-two covers. Pantagruel sat 
at the head, Epistemon at the bottom, and Panurge in the 
middle, opposite an immense silver tureen, which would hold 
fifty gallons of soup. The wise men of Pontemaca then 
took their seats according to seniority. Every countenance 
glistened with delight ; the music struck up ; the dishes were 
uncovered. Panurge had enough to do to handle the im- 
mense silver ladle: Pantagruel and Epistemon had no time 
for eating, they were fully employed in carving. The bill 



MR. TREND'S BURLESQUE. 213 

of fare announced the names of a hundred different dishes. 
From Panurge's ladle came into the soup plate as much as 
he took every time out of the tureen ; and as it was the rule 
of the court that every one should appear to eat, as long as 
he sat at table, there was the clattering of nine and thirty 
spoons against the silver soup-plates for a quarter of an 
hour. They were then removed, and knives and forks were 
in motion for half an hour. Glasses were continually handed 
round in the mean time, and then everything was removed, 
except the great tureen of soup. The second course was 
now served up, in dispatching which half an hour was con- 
sumed ; and at the conclusion the wise men of Pontemaca 
had just as much in their stomachs as Pantagruel in his 
head from their address: for nothing was cooked up for 
them in every possible shape that Panurge could devise. 

"Wine-glasses, large decanters, fruit dishes, and plates 
were now set on. Pantagruel and Epistemon alternately 
gave bumper toasts: the University of Pontemaca, the eye 
of the world, the mother of taste and good sense and uni- 
versal learning, the patroness of utility, and the second only 
to Pantagruel in wisdom and virtue (for these were her 
titles), was drank standing with thrice three times three, 
and huzzas and clattering of glasses ; but to such wine the 
wise men of Pontemaca had not been accustomed; and 
though Pantagruel did not suffer one to rise from table till 
the eighty-first glass had been emptied, not even the weak- 
est headed master of arts felt his head in the least indis- 
posed. The decanters indeed were often removed, but they 
were brought back replenished, filled always with nothing. 

"Silence was now proclaimed, and in a trice Panurge 
leaped into the large silver tureen. Thence he made his 
bows to Pantagruel and the whole company, and commenced 
an oration of signs, which lasted an hour and a half, and in 
which he went over all the matter contained in the Ponte- 
maca address ; and though the wise men looked very serious 
during the whole time, Pantagruel himself and his whole 



214 A BUDGET OF PARADOXES. 

court could not help indulging in repeated bursts of laugh- 
ter. It was universally acknowledged that he excelled him- 
self, and that the arguments by which he beat the English 
masters of arts at Paris were nothing to the exquisite selec- 
tion of attitudes which he this day assumed. The greatest 
shouts of applause were excited when he was running thrice 
round the tureen on its rim, with his left hand holding his 
nose, and the other exercising itself nine and thirty times 
on his back. In this attitude he concluded with his back to 
the professor of mathematics ; and at the instant he gave his 
last flap, by a sudden jump, and turning heels over head in 
the air, he presented himself face to face to the professor, 
and standing on his left leg, with his left hand holding his 
nose, he presented to him, in a white satin bag, Pantagruel's 
royal decree. Then advancing his right leg, he fixed it on 
the professor's head, and after three turns, in which he 
clapped his sides with both hands thrice three times, down 
he leaped, and Pantagruel, Epistemon, and himself took 
their leaves of the wise men of Pontemaca. 

"The wise men now retired, and by royal orders were 
accompanied by a guard, and according to the etiquette of 
the court, no one having a royal order could stop at any 
public house till it was delivered. The procession arrived 
at Pontemaca at nine o'clock the next morning, and the 
sound of bells from every church and college announced 
their arrival. The congregation was assembled ; the royal 
decree was saluted in the same manner as if his highness 
had been there in person; and after the proper ceremonies 
had been performed, the satin bag was opened exactly at 
twelve o'clock. A finely emblazoned roll was drawn forth, 
and the public orator read to the gaping assembly the fol- 
lowing words: 

" 'They who can make something out of nothing shall 
have nothing to eat at the court of PANTAGRUEL/ " 



MR. FREND'S BURLESQUE. 215 

ORIGIN of the ENGLISH LANGUAGE, related by a SWEDE. 

"Some months ago in a party in Holland, consisting of 
natives of various countries, the merit of their respective 
languages became a topic of conversation. A Swede, who 
had been a great traveler, and could converse in most of 
the modern languages of Europe, laughed very heartily at 
an Englishman, who had ventured to speak in praise of the 
tongue of his dear country. I never had any trouble, says he, 
in learning English. To my very great surprise, the moment 
I sat foot on shore at Gravesend, I found out, that I could 
understand, with very little trouble, every word that was 
said. It was a mere jargon, made up of German, French, 
and Italian, with now and then a word from the Spanish, 
Latin or Greek. I had only to bring my mouth to their 
mode of speaking, which was done with ease in less than a 
week, and I was everywhere taken for a true-born English- 
man ; a privilege by the way of no small importance in a 
country, where each man, God knows why, thinks his foggy 
island superior to any other part of the world : and though 
his door is never free from some dun or other coming for 
a tax, and if he steps out of it he is sure to be knocked down 
or to have his pocket picked, yet he has the insolence to 
think every foreigner a miserable slave, and his country the 
seat of everything wretched. They may talk of liberty as 
they please, but Spain or Turkey for my money: barring 
the bowstring and the inquisition, they are the most com- 
fortable countries under heaven, and you need not be afraid 
of either, if you do not talk of religion and politics. I do 
not see much difference too in this respect in England, for 
when I was there, one of their most eminent men for learn- 
ing was put in prison for a couple of years, and got his death 
for translating one of ^Esop's fables into English, which 
every child in Spain and Turkey is taught, as soon as he 
comes out of his leading strings. Here all the company 
unanimously cried out against the Swede, that it was im- 



216 A BUDGET OF PARADOXES. 

possible : for in England, the land of liberty, the only thing 
its worst enemies could say against it, was, that they paid 
for their liberty a much greater price than it was worth. 
Every man there had a fair trial according to laws, which 
everybody could understand ; and the judges were cool, pa- 
tient, discerning men, who never took the part of the crown 
against the prisoner, but gave him every assistance possible 
for his defense. 

"The Swede was borne down, but not convinced; and 
he seemed determined to spit out all his venom. Well, says 
he, at any rate you will not deny that the English have not 
got a language of their own, and that they came by it in a 
very odd way. Of this at least I am certain, for the whole 
history was related to me by a witch in Lapland, whilst I 
was bargaining for a wind. Here the company were all in 
unison again for the story. 

"In ancient times, said the old hag, the English occupied 
a spot in Tartary, where they lived sulkily by themselves, 
unknowing and unknown. By a great convulsion that took 
place in China, the inhabitants of that and the adjoining 
parts of Tartary were driven from their seats, and after 
various wanderings took up their abode in Germany. During 
this time nobody could understand the English, for they 
did not talk, but hissed like so many snakes. The poor 
people felt uneasy under this circumstance, and in one of 
their parliaments, or rather hissing meetings, it was deter- 
mined to seek a remedy: and an embassy was sent to some 
of our sisterhood then living on Mount Hecla. They were 
put to a nonplus, and summoned the Devil to their relief. 
To him the English presented their petitions, and explained 
their sad case ; and he, upon certain conditions, promised to 
befriend them, and to give them a language. The poor 
Devil was little aware of what he had promised ; but he is, 
as all the world knows, a man of too much honor to break 
his word. Up and down the world then he went in quest 
of this new language: visited all the universities, and all 



MR. TREND'S BURLESQUE. 217 

the schools, and all the courts of law, and all the play-houses, 
and all the prisons ; never was poor devil so fagged. It 
would have made your heart bleed to see him. Thrice did 
he go round the earth in every parallel of latitude ; and at 
last, wearied and jaded out, back came he to Hecla in de- 
spair, and would have thrown himself into the volcano, if 
he had been made of combustible materials. Luckily at 
that time our sisters were engaged in settling the balance 
of Europe; and whilst they were looking over projects, and 
counter-projects, and ultimatums, and post ultimatums, the 
poor Devil, unable to assist them was groaning in a corner 
and ruminating over his sad condition. 

"On a sudden, a hellish joy overspread his countenance ; 
up he jumped, and, like Archimedes of old, ran like a mad- 
man amongst the throng, turning over tables, and papers, 
and witches, roaring out for a full hour together nothing 
else but 'tis found, 'tis found! Away were sent the sister- 
hood in every direction, some to traverse all the corners of 
the earth, and others to prepare a larger caldron than had 
ever yet been set upon Hecla. The affairs of Europe were 
at a stand : its balance was thrown aside ; prime ministers 
and ambassadors were everywhere in the utmost confusion ; 
and, by the way, they have never been able to find the 
balance since that time, and all the fine speeches upon the 
subject, with which your newspapers are every now and then 
filled, are all mere hocus-pocus and rhodomontade. How- 
ever, the caldron was soon set on, and the air was darkened 
by witches riding on broomsticks, bringing a couple of folios 
under each arm, and across each shoulder. I remember the 
time exactly: it was just as the council of Nice had broken 
up, so that they got books and papers there dog cheap ; but 
it was a bad thing for the poor English, as these were the 
worst materials that entered into the caldron. Besides, as the 
Devil wanted some amusement, and had not seen an account 
of the transactions of this famous council, he had all the books 
brought from it laid before him, and split his sides almost 



218 A BUDGET OF PARADOXES. 

with laughing, whilst he was reading the speeches and decrees 
of so many of his old friends and acquaintances. All this 
while the witches were depositing their loads in the great 
caldron. There were books from the Dalai Lama, and from 
China : there were books from the Hindoos, and tallies from 
the Caffres: there were paintings from Mexico, and rocks 
of hieroglyphics from Egypt: the last country supplied be- 
sides the swathings of two thousand mummies, and four- 
fifths of the famed library of Alexandria. Bubble ! bubble ! 
toil and trouble ! never was a day of more labor and anxiety ; 
and if our good master had but flung in the Greek books at 
the proper time, they would have made a complete job of 
it. He was a little too impatient : as the caldron frothed up, 
he skimmed it off with a great ladle, and filled some thou- 
sands of our wind-bags with the froth, which the English 
with great joy carried back to their own country. These 
bags were sent to every district: the chiefs first took their 
fill, and then the common people ; hence they now speak 
a language which no foreigner can understand, unless he 
has learned half a dozen other languages; and the poor 
people, not one in ten, understand a third part of what is 
said to them. The hissing, however, they have not entirely 
got rid of, and every seven years, when the Devil, according 
to agreement, pays them a visit, they entertain him at their 
common halls and county meetings with their original lan- 
guage. 

"The good-natured old hag told me several other circum- 
stances, relative to this curious transaction, which, as there 
is an Englishman in company, it will be prudent to pass 
over in silence: but I cannot help mentioning one thing 
which she told me as a very great secret. You know, says 
she to me, that the English have more religions among them 
than any other nation in Europe, and that there is more 
teaching and sermonizing with them than in any other coun- 
try. The fact is this ; it matters not who gets up to teach 
them, the hard words of the Greek were not sufficiently 



ON YOUTHFUL PRODIGIES. 219 

boiled, and whenever they get into a sentence, the poor 
people's brains are turned, and they know no more what the 
preacher is talking about, than if he harangued them in 
Arabic. Take my word for it if you please ; but if not, when 
you get to England, desire the bettermost sort of people 
that you are acquainted with to read to you an act of parlia- 
ment, which of course is written in the clearest and plainest 
style in which anything can be written, and you will find 
that not one in ten will be able to make tolerable sense of it. 
The language would have been an excellent language, if 
it had not been for the council of Nice, and the words had 
been well boiled. 

"Here the company burst out into a fit of laughter. The 
Englishman got up and shook hands with the Swede : si non 
e vero, said he, e ben trovato.* But, however I may laugh at 
it here, I would not advise you to tell this story on the other 
side of the water. So here's a bumper to Old England for 
ever, and God save the king." 

ON YOUTHFUL PRODIGIES. 

The accounts given of extraordinary children and adoles- 
cents frequently defy credence. 1 I will give two well-attested 
instances. 

The celebrated mathematician Alexis Claude Clairault 
(now Clairaut) 2 was certainly born in May, 1713. His treat- 
ise on curves of double curvature (printed in 1731)3 received 

8 "If it is not true it is a good invention." A well-known Italian 
proverb. 

1 See page 86, note 3. 

2 He was born at Paris in 1713, and died there in 1765. 

8 Recherche s sur les courbes a double courbure, Paris, 1731. Clai- 
raut was then only eighteen, and was in the same year made a mem- 
ber of the Academic des sciences. His Element de geometric ap- 
peared in 1741. Meantime he had taken part in the measurement of 
a degree in Lapland (1736-1737). His Trait e de la -figure de la 
terre was published in 1741. The Academy of St. Petersburg 
awarded him a prize for his Theorie de la lune (1750). His various 
works on comets are well known, particularly his Theorie du mouve- 
ment des cometes (1760) in which he applied the "problem of three 
bodies" to Halley's comet as retarded by Jupiter and Saturn. 



220 A BUDGET OF PARADOXES. 

the approbation of the Academy of Sciences, August 23, 
1729. Fontenelle, in his certificate of this, calls the author 
sixteen years of age, and does not strive to exaggerate the 
wonder, as he might have done, by reminding his readers 
that this work, of original and sustained mathematical in- 
vestigation, must have been coming from the pen at the 
ages of fourteen and fifteen. The truth was, as attested by 
De Molieres, 4 Clairaut had given public proofs of his power 
at twelve years old. His age being thus publicly certified, 
all doubt is removed: say he had been though great won- 
der would still have been left twenty-one instead of six- 
teen, his appearance, and the remembrances of his friends, 
schoolfellows, etc., would have made it utterly hopeless to 
knock off five years of that age while he was on view in 
Paris as a young lion. De Molieres, who examined the 
work officially for the Garde des Sceaux, is transported 
beyond the bounds of official gravity, and says that it "ne 
merite pas seulement d'etre imprime, mais d'etre admire 
comme un prodige d'imagination, de conception, et de ca- 
pacite." 5 

That Blaise Pascal was born in June, 1623, is per- 
fectly well established and uncontested. 6 That he wrote his 
conic sections at the age of sixteen might be difficult to 
establish, though tolerably well attested, if it were not for 

4 Joseph Privat, Abbe de Molieres (1677-1742), was a priest of 
the Congregation of the Oratorium. In 1723 he became a professor 
in the College de France. He was well known as an astronomer and 
a mathematician, and wrote in defense of Descartes's theory of 
vortices (1728, 1729). He also contributed to the methods of find- 
ing prime numbers (1705). 

B "Deserves not only to be printed, but to be admired as a marvel 
of imagination, of understanding, and of ability." 

6 Blaise Pascal (1623-1662), the well-known French philosopher 
and mathematician. He lived for some time with the Port Royalists, 
and defended them against the Jesuits in his Provincial Letters. 
Among his works are the following: Essai pour les coniques (1640) ; 
Recit de la grande experience de I'equilibre des liqueurs (1648), de- 
scribing his experiment in finding altitudes by barometric readings ; 
Histoire de la roulette (1658); Traite du triangle arithmetique 
(1665) ; Aleae geometria (1654). 



ON YOUTHFUL PRODIGIES. 221 

one circumstance, for the book was not published. The 
celebrated theorem, "Pascal's hexagram," 7 makes all the 
rest come very easy. Now Curabelle, 8 in a work published 
in 1644, sneers at Desargues, 9 whom he quotes, for having, 
in 1642, deferred a discussion until "cette grande proposition 
nommee le Pascale verra le jour." 10 That is, by the time 
Pascal was nineteen, the hexagram was circulating under 
a name derived from the author. The common story about 
Pascal, given by his sister, 11 is an absurdity which no doubt 
has prejudiced many against tales of early proficiency. He 
is made, when quite a boy, to invent geometry in the order 
of Euclid's propositions: as if that order were natural se- 
quence of investigation. The hexagram at ten years old 
would be a hundred times less unlikely. 

The instances named are painfully astonishing: I give 
one which has fallen out of sight, because it will preserve 
an imperfect biography. John Wilson 12 is Wilson of that 

7 This proposition shows that if a hexagon is inscribed in a 
conic (in particular a circle) and the opposite sides are produced 
to meet, the three points determined by their intersections will be in 
the same straight line. 

8 Jacques Curabelle, Examen des (Euvres du Sr. Desargues, Paris, 
1644. He also published without date a work entitled: Foiblesse 
pitoyable du Sr. G. Desargues employee contre I'examen fait de ses 
ceuvres. 

9 See page 119, note 2. 

10 Until "this great proposition called Pascal's should see the 
light." 

11 The story is that his father, Etienne Pascal, did not wish him 
to study geometry until he was thoroughly grounded in Latin and 
Greek. Having heard the nature of the subject, however, he began 
at the age of twelve to construct figures by himself, drawing them 
on the floor with a piece of charcoal. When his father discovered 
what he was doing he was attempting to demonstrate that the sum 
of the angles of a triangle equals two right angles. The story is 
given by his sister, Mme. Perier. 

"Sir John Wilson (1741-1793) was knighted in 1786 and became 
Commissioner of the Great Seal in 1792. He was a lawyer and jurist 
of recognized merit. He stated his theorem without proof, the first 
demonstration having been given by Lagrange in the Memoirs of 
the Berlin Academy for 1771, Demonstration d'un theoreme nou- 
veau concernant les nombres premiers. Euler also gave a proof in 
his Miscellanea Analytica (1773). Fermat's works should be con- 
sulted in connection with the early history of this theorem. 



222 A BUDGET OF PARADOXES. 

Ilk, that is, of "Wilson's Theorem." It is this: if p be a 
prime number, the product of all the numbers up to p 1, in- 
creased by 1, is divisible without remainder by p. All 
mathematicians know this as Wilson's theorem, but few 
know who Wilson was. He was born August 6, 1741, at 
the Howe in Applethwaite, and he was heir to a small 
estate at Troutbeck in Westmoreland. He was sent to 
Peterhouse, at Cambridge, and while an undergraduate was 
considered stronger in algebra than any one in the Uni- 
versity, except Professor Waring, one of the most powerful 
algebraists of the century. 13 He was the senior wrangler of 
1761, and was then for some time a private tutor. When 
Paley, 14 then in his third year, determined to make a push 
for the senior wranglership, which he got, Wilson was 
recommended to him as a tutor. Both were ardent in their 
work, except that sometimes Paley, when he came for his 
lesson, would find "Gone a fishing" written on his tutor's 
outer door: which was insult added to injury, for Paley 
was very fond of fishing. Wilson soon left Cambridge, and 
went to the bar. He practised on the northern circuit with 
great success ; and, one day, while passing his vacation on 
his little property at Troutbeck, he received information, to 
his great surprise, that Lord Thurlow, 15 with whom he had 

"He wrote, in 1760, a tract in defense of Waring, a point of 
whose algebra had been assailed by a Dr. Powell. Waring wrote 
another tract of the same date. A. De M. 

William Samuel Powell (1717-1775) was at this time a fellow 
of St. John's College, Cambridge. In 1765 he became Vice Chan- 
cellor of the University. Waring was a Magdalene man, and while 
candidate for the Lucasian professorship he circulated privately his 
Miscellanea Analytica. Powell attacked this in his Observations on 
the First Chapter of a Book called Miscellanea (1760). This attack 
was probably in the interest of another candidate, a man of his own 
college (St. John's), William Ludlam. 

"William Paley (1743-1805) was afterwards a tutor at Christ's 
College, Cambridge. He never contributed anything to mathematics, 
but his Evidences of Christianity (1794) was long considered some- 
what of a classic. He also wrote Principles of Morality and Poli- 
tics (1785), and Natural Theology (1802). 

15 Edward, first Baron Thurlow (1731-1806) is known to Ameri- 
cans because of his strong support of the Royal prerogative during 



ON YOUTHFUL PRODIGIES. 223 

no acquaintance, had recommended him to be a Judge of 
the Court of Common Pleas. He died, Oct. 18, 1793, with 
a very high reputation as a lawyer and a Judge. These 
facts are partly from Meadley's Life of Paley no doubt from 
Paley himself, partly from the Gentleman's Magazine, and 
fsom an epitaph written by Bishop Watson. 17 Wilson did 
not publish anything: the theorem by which he has cut 
his name in the theory of numbers was communicated to 
Waring, by whom it was published. He married, in 1788, 
a daughter of Serjeant Adair, 18 and left issue. Had a family, 
many will say : but a man and his wife are a family, even 
without children. An actuary may be allowed to be accurate 
in this matter, of which I was reminded by what an actuary 
wrote of another actuary. William Morgan, 19 in the life of 
his uncle Dr. Richard Price, 20 says that the Doctor and his 

the Revolution. He was a favorite of George III, and became 
Lord Chancellor in 1778. 

"George Wilson Meadley (1774-1818) published his Memoirs 
of .... Paley in 1809. He also published Memoirs of Algernon Sid- 
ney in 1813. He was a merchant and banker, and had traveled ex- 
tensively in Europe and the East. He was a convert to unitarianism, 
to which sect Paley had a strong leaning. 

"Watson (1737-1816) was a strange kind of man for a bishop- 
ric. He was professor of chemistry at Cambridge (1764) at the age 
of twenty-seven. It was his experiments that led to the invention 
of the black-bulb thermometer. He is said to have saved the gov- 
ernment 100,000 a year by his advice on the manufacture of gun- 
powder. Even after he became professor of divinity at Cambridge 
(1771) he published four volumes of Chemical Essays (vol. I, 1781). 
He became Bishop of Llandaff in 1782. 

18 James Adair (died in 1798) was counsel for the defense in 
the trial of the publishers of the Letters of Junius (1771). As King's 
Serjeant he assisted in prosecuting Hardy and Home Tooke. 

19 Morgan (1750-1833) was actuary of the Equitable Assurance 
Society of London (1774-1830), and it was to his great abilities that 
the success of that company was due at a time when other corpora- 
tions of similar kind were meeting with disaster. The Royal So- 
ciety awarded him a medal (1783) for a paper on Probability of 
Survivorship. He wrote several important works on insurance and 
finance. 

20 Dr. Price (1723-1791) was a non-conformist minister and a 
writer on ethics, economics, politics, and insurance. He was a de- 
fender of the American Revolution and a personal friend of Frank- 
lin. In 1778 Congress invited him to America to assist in the finan- 



224 A BUDGET OF PARADOXES. 

wife were "never blessed with an addition to their family." 
I never met with such accuracy elsewhere. Of William 
Morgan I add that my surname and pursuits have some- 
times, to my credit be it said, made a confusion between 
him and me. Dates are nothing to the mistaken ; the last 
three years of Morgan's life were the first three years of 
my actuary-life (1830-33). The mistake was to my advan- 
tage as well as to my credit. I owe to it the acquaintance 
of one of the noblest of the human race, I mean Elizabeth 
Fry, 21 who came to me for advice about a philanthropic de- 
sign, which involved life questions, under a general im- 
pression that some Morgan had attended to such things. 22 

cial administration of the new republic, but he declined. His famous 
sermon on the French Revolution is said to have inspired Burke's 
Reflections on the Revolution in France, 

21 Elizabeth Gurney (1780-1845), a Quaker, who married Joseph 
Fry (1800), a London merchant. She was the prime mover in the 
Association for^ the Improvement of the Female Prisoners in New- 
gate, founded in 1817. Her influence in prison reform extended 
throughout Europe, and she visited the prisons of many countries 
in her efforts to improve the conditions of penal servitude. The 
friendship of Mrs. Fry with the De Morgans began in 1837. Her 
scheme for a female benefit society proved worthless from the 
actuarial standpoint, and would have been disastrous to all con- 
cerned if it had been carried out, and it was therefore fortunate 
that De Morgan ^was consulted in time. Mrs. De Morgan speaks of 
the consultation in these words : "My husband, who was very sensi- 
tive on such points, was charmed with Mrs. Fry's voice and manner 
as much as by the simple self-forgetfulness with which she entered 
into this business ; her own very uncomfortable share of it not being 
felt as an element in the question, as long as she could be useful in 
promoting good or preventing mischief. I can see her now as she 
came into our room, took off her little round Quaker cap, and laying 
it down, _went at once into the matter. 'I have followed thy advice, 
and I think nothing further can be done in this case; but all harm 
is prevented.' In the following year I had an opportunity of seeing 
the _ effect of her most musical tones. I visited her at Stratford, 
taking my little baby and nurse with me, to consult her on some 
articles on prison discipline, which I had written for a periodical. 
The baby three months old was restless, and the nurse could not 
quiet her, neither could I entirely, until Mrs. Fry began to read 
something connected with the subject of my visit, when the infant, 
fixing her large eyes on the reader, lay listening till she fell asleep." 
Memoirs, p. 91. 

22 Mrs. Fry certainly believed that the writer was the old actuary 
of the Equitable, when she first consulted him upon the benevolent 
Assurance project; but we were introduced to her by our old and 



NEWTON AGAIN OVERTHROWN. 225 



NEWTON AGAIN OVERTHROWN. 

A treatise on the sublime science of heliography, satisfactorily 
demonstrating our great orb of light, the sun, to be absolutely 
no other than a body of ice ! Overturning all the received 
systems of the universe hitherto extant ; proving the celebrated 
and indefatigable Sir Isaac Newton, in his theory of the solar 
system, to be as far distant from the truth, as many of the 
heathen authors of Greece and Rome. By Charles Palmer, 1 
Gent. London, 1798, 8vo. 

Mr. Palmer burned some tobacco with a burning glass, 
saw that a lens of ice would do as well, and then says: 

"If we admit that the sun could be removed, and a ter- 
restrial body of ice placed in its stead, it would produce the 
same effect. The sun is a crystaline body receiving the 
radiance of God, and operates on this earth in a similar 
manner as the light of the sun does when applied to a con- 
vex mirror or glass." 

Nov. 10, 1801. The Rev. Thomas Cormouls, 2 minister 
of Tettenhall, addressed a letter to Sir Wm. Herschel, from 
which I extract the following: 

"Here it may be asked, then, how came the doctrines of 
Newton to solve all astronomic Phenomina, and all problems 
concerning the same, both a parte ante and a parte post. 3 It 
is answered that he certainly wrought the principles he made 
use of into strickt analogy with the real Phenomina of the 
heavens, and that the rules and results arizing from them 

dear friend Lady Noel Byron, by whom she had been long known 
and venerated, and who referred her to Mr. De Morgan for advice. 
An unusual degree of confidence in, and appreciation of each other, 
arose on their first meeting between the two, who had so much that 
was externally different, and so much that was essentially alike, in 
their natures. S. E. De M. 

Anne Isabella Milbanke (1792-1860) married Lord Byron in 
1815, when both took the additional name of Noel, her mother's 
name. They were separated in 1816. 

1 An obscure writer not mentioned in the ordinary biographies. 

2 Not mentioned in the ordinary biographies, and for obvious 

reasons. 



3 u 



"Before" and "after.' 



226 A BUDGET OF PARADOXES. 

agree with them and resolve accurately all questions con- 
cerning them. Though they are not fact and true, or nature, 
but analogous to it, in the manner of the artificial numbers 
of logarithms, sines, &c. A very important question arises 
here, Did Newton mean to impose upon the world? By no 
means : he received and used the doctrines reddy formed ; 
he did a little extend and contract his principles when 
wanted, and commit a few oversights of consequences. But 
when he was very much advanced in life, he suspected the 
fundamental nullity of them: but I have from a certain 
anecdote strong ground to believe that he knew it before 
his decease and intended to have retracted his error. But, 
however, somebody did deceive, if not wilfully, negligently 
at least. That was a man to whom the world has great 
obligations too. It was no less a philosopher than Galileo." 
That Newton wanted to retract before his death, is a 
notion not uncommon among paradoxers. Nevertheless, 
there is no retraction in the third edition of the Principia, 
published when Newton was eighty-four years old! The 
moral of the above is, that a gentleman who prefers in- 
structing William Herschel to learning how to spell, may 
find a proper niche in a proper place, for warning to others. 
It seems that gravitation is not truth, but only the loga- 
rithm of it. 

BISHOPS AS PARADOXERS. 

The mathematical and philosophical works of the Right Rev. 
John Wilkins 1 .... In two volumes. London, 1802, 8vo. 

This work, or at least part of the edition all for aught 
I know is printed on wood; that is, on paper made from 
wood-pulp. It has a rough surface ; and when held before 
a candle is of very unequal transparency. There is in it a 
reprint of the works on the earth and moon. The discourse 
on the possibility of going to the moon, in this and the 
edition of 1640, is incorporated : but from the account in the 

*On Bishop Wilkins see note I on page 100. 



BISHOPS AS PARADOXERS. 227 

life prefixed, and a mention by D'Israeli, I should suppose 
that it had originally a separate title-page, and some circu- 
lation as a separate tract. Wilkins treats this subject half 
seriously, half jocosely; he has evidently not quite made 
up his mind. He is clear that "arts are not yet come to 
their solstice," and that posterity will bring hidden things 
to light. As to the difficulty of carrying food, he thinks, 
scoffing Puritan that he is, the Papists may be trained to fast 
the voyage, or may find the bread of their Eucharist "serve 
well enough for their viaticum." 2 He also puts the case 
that the story of Domingo Gonsales may be realized, namely, 
that wild geese find their way to the moon. It will be re- 
membered to use the usual substitute for, It has been for- 
gotten that the posthumous work of Bishop Francis God- 
win 3 of Llandaff was published in 1638, the very year of 
Wilkins's first edition, in time for him to mention it at the 
end. Godwin makes Domingo Gonsales get to the moon in 
a chariot drawn by wild geese, and, as old books would say, 
discourses fully on that head. It is not a little amusing that 
Wilkins should* have been seriously accused of plagiarizing 
Godwin, Wilkins writing in earnest, or nearly so, and God- 
win writing fiction. It may serve to show philosophers how 
very near pure speculation comes to fable. From the sublime 
to the ridiculous is but a step: which is the sublime, and 
which the ridiculous, every one must settle for himself. 
With me, good fiction is the sublime, and bad speculation 
the ridiculous. The number of bishops in my list is small. 
I might, had I possessed the book, have opened the list of 
quadrators with an Archbishop of Canterbury, or at least 
with a divine who was not wholly not archbishop. Thomas 
Bradwardine 4 (Bragvardinus, Bragadinus) was elected in 

2 Pro vision for a journey. 

3 See note 3 on page 103. 

4 Thomas Bradwardine (1290-1349), known as Doct or Profundus, 
proctor and professor of theology at Oxford, and afterwards Chan- 
cellor of St. Paul's and confessor to Edward III. The English 
ascribed their success at Crecy to his prayers. 



228 A BUDGET OF PARADOXES. 

1348 ; the Pope put in another, who died unconsecrated ; and 
Bradwardine was again elected in 1349, and lived five weeks 
longer, dying, I suppose, unconfirmed and unconsecrated. 5 
Leland says he held the see a year, unus tantum annulus* 
which seems to be a confusion : the whole business, from the 
first election, took about a year. He squared the circle, and 
his performance was printed at Paris in 1494. I have never 
seen it, nor any work of the author, except a tract on pro- 
portion. 

As Bradwardine's works are very scarce indeed, I give 
two titles from one of the Libri catalogues. 



"ARITHMETIC. BRAUARDINI (Thomae) Arithmetica speculativa 
revisa et correcta a Petro Sanchez Ciruelo Aragonesi, black 
letter, elegant woodcut title-page, VERY RARE, folio. Parisiis, per 
Thomam Anguelast (prv Olivier Senant), s.a. circa I5io. 7 

"This book, by Thomas Bradwardine, Archbishop of 
Canterbury must be exceedingly scarce as it has escaped 
the notice of Professor De Morgan, who, in his Arithmetical 
Books, speaks of a treatise of the same author on propor- 
tions, 8 printed at Vienna in 1515, but does not mention the 
present work. 

5 He was consecrated Archbishop of Canterbury by the Pope at 
Avignon, July 13, 1349, and died of the plague at London in the 
same year. 

6 "One paltry little year." 

7 The title is carelessly copied, as is so frequently the case in 
catalogues, even of the Libri class. It should read: Arithmetica 
thome brauardini.\\Olivier Senant\\Venum exponuntur ab Oliuiario 
senant in vico diui Jacobi sub signo beate Barbare sedente. The colo- 
phon reads: Explicit arithmetica speculatiua thoe brauardini bn re- 
uisa et correcta a Petro sanchez Ciruelo aragoncnsi mathematicas 
legete Parisius, ipressa per Thoma anguelart. There were Paris edi- 
tions of 1495, 1496, 1498, s. a. (c. 1500), 1502, 1504, 1505, s.a. (c. 
JSio), 1512, 1530, a Valencia edition of 1503, two Wittenberg edi- 
tions^ of 1534 and 1536, and doubtless several others. The work is 
not "very rare," although of course no works of that period are 
common. See the editor's Rara Arithmetica, page 61. 

8 This is his Tractatus de proportionibus, Paris, 1495; Venice, 
1505; Vienna, 1515, with other editions. 



THE QUESTION OF PARALLELS. 229 



"Bradwardine (Archbp. T.). Brauardini (Thomae) Geometria 
speculativa, com Tractatu de Quadratura Circuli bene revisa 
a Petro Sanchez Ciruelo, SCARCE, folio. Parisiis, J. Petit, i$n. 9 

"In this work we find the polygones etoiles, 10 see Chasles 
(Apergu, pp. 480, 487, 521, 523, &c.) on the merit of the 
discoveries of this English mathematician, who was Arch- 
bishop of Canterbury in the xivth Century (tempore Edward 
III. A. D. 1349) ; and who applied geometry to theology. 
M. Chasles says that the present work of Bradwardine con- 
tains 'Une theorie nouvelle qui doit faire honneur au xive 
Siecle.' mi 

The titles do not make it quite sure that Bradwardine 
is the quadrator ; it may be Peter Sanchez after all. 12 

THE QUESTION OF PARALLELS. 

Nouvelle theorie des paralleles. Par Adolphe Kircher 1 [so" 
signed at the end of the appendix], Paris, 1803, 8vo. 

An alleged emendation of Legendre. 2 The author refers 

9 The colophon of the 1495 edition reads: Et sic explicit^ Geo- 
metria Thome brauardini cu tractatulo de quadrature, circuit bene 
reuisa a Petro sanchez ciruelo : operaqz Guidonis mercatoris dili- 
getissime impresse parisi in capo gaillardi. Anno dni. 1495. die. 
20. maij. 

This Petro Ciruelo was born in Arragon, and died in 1560 at 
Salamanca. He studied mathematics and philosophy at Paris, and 
took the doctor's degree there. He taught at the University of 
Alcala and became canon of the Cathedral at Salamanca. Besides 
his editions of Bradwardine he wrote several works, among them 
the Liber arithmeticae practicae qui dicitur algorithmus (Paris, 
1495) and the Cursus quatuor mathematicarum artium liberalium 
(Alcala, 1516). 

10 Star polygons, a subject of considerable study in the later 
Middle Ages. See note I on page 44. 

1 "A new theory that adds lustre to the fourteenth century." 

"There is nothing in the edition of 1495 that leads to this con- 
clusion. 

1 The full title is : Nouvelle theorie des paralleles, avec un appen- 
dice contenant la maniere de perfectionner la theorie des paralleles 
de A. M. Legendre. The author had no standing as a scientist. 

2 Adrien Marie Legendre (1752-1833) was one of the great 
mathematicians of the opening of the nineteenth century. His Ele- 
ments de geometric (1794) had great influence on the geometry of 



230 A BUDGET OF PARADOXES. 

to attempts by Hoffman, 3 1801, by Hauff, 4 1799, and to a 
work of Karsten, 5 or at least a theory of Karsten, contained 
in "Tentamen novae parallelarum theoriae notione situs fun- 
datae; auctore G. C. Schwal, 6 Stuttgardae, 1801, en 8 vo- 
lumes." Surely this is a misprint; eight volumes on the 
theory of parallels ? If there be such a work, I trust I and 
it may never meet, though ever so far produced. 

the United States. His Essai sur la theorie des nombres (1798) is 
one of the classics upon the subject. The work to which Kircher 
refers is the Notcvelle theorie des paralleles (1803), in which the 
attempt is made to avoid using Euclid's postulate of parallels, the 
result being merely the substitution of another assumption that was 
even more unsatisfactory. The best presentations of the general 
theory are W. B. Frankland's Theories of Parallelism, Cambridge, 
1910, and Engel and Stacker's Die Theorie der Parallellinien von 
Euclid bis auf Gauss, Leipsic, 1895. Legendre published a second 
work on the theory the year of his death, Reflexions sur .... la 
theorie des paralleles (1833). His other works include the Nou- 
velles methodes pour la determination des orbites des cometes (1805), 
in which he uses the method of least squares ; the Traite des fonc- 
tions elliptiques et des integrates (1827-1832), and the Exercises de 
calcul integral (1811, 1816, 1817). 

'Johann Joseph Ignatz von Hoffmann (1777-1866), professor 
of mathematics at Aschaffenburg, published his Theorie der Parallel- 
linien in 1801. He supplemented this by his Kritik der Parallelen- 
Theorie in 1807, and his Das eilfte Axiom der Elemente des Euclidis 
neu bewiesen in 1859. He wrote other works on mathematics, but 
none of his contributions was of any importance. 

4 Johann Karl Friedrich Hauff (1766-1846) was successively 
professor of mathematics at Marburg, director of the polytechnic 
school at Augsburg, professor at the Gymnasium at Cologne, and 
professor of mathematics and physics at Ghent. The work to which 
Kircher refers is his memoirs on the Euclidean Theorie der Paral- 
lelen in Hindenburg's Archiv, vol. Ill (1799), an article of no merit 
in the general theory. 

6 Wenceslaus Johann Gustav Karsten (1732-1787) was professor 
of logic at Rostock (1758) and Butzow (1760), and later became 
professor of mathematics and physics at Halle. His work on paral- 
lels is the Versuch einer vollig berichtigten Theorie der Parallel- 
linien (1779). He also wrote a work entitled Anfangsgriinde der 
mathematischen Wissenschaften (1780), but neither of these works 
was more than mediocre. 

6 Johann Christoph Schwab (not Schwal) was born in 1743 and 
died in 1821. He was professor at the Karlsschule at Stuttgart. 
De Morgan's wish was met, for the catalogues give "c. fig. 8," so 
that it evidently had eight illustrations instead of eight volumes. 
He wrote several other works on the principles of geometry, none 
of any importance. 



A PATRIOTIC PARADOX. 231 

Soluzione .... della quadratura del Circolo. By Gaetano 
Rossi. 7 London, 1804, 8vo. 

The three remarkable points of this book are, that the 
household of the Prince of Wales took ten copies, Signora 
Grassini 8 sixteen, and that the circumference is 3% diam- 
eters. That is, the appetite of Grassini for quadrature ex- 
ceeded that of the whole household (loggia) of the Prince 
of Wales in the ratio in which the semi-circumference ex- 
ceeds the diameter. And these are the first two in the list 
of subscribers. Did the author see this theorem? 

A PATRIOTIC PARADOX. 

Britain independent of commerce; or proofs, deduced from an 
investigation into the true cause of the wealth of nations, 
that our riches, prosperity, and power are derived from sources 
inherent in ourselves, and would not be affected, even though 
our commerce were annihilated. By Wm. Spence. 1 4th edi- 
tion, 1808, 8vo. 

A patriotic paradox, being in alleviation of the Com- 
merce panic which the measures of Napoleon I. who felt 
our Commerce, while Mr. Spence only saw it had awak- 
ened. In this very month (August, 1866), the Pres. Brit. 
Assoc. has applied a similar salve to the coal panic ; it is fit 
that science, which rubbed the sore, should find a plaster. 
We ought to have an iron panic and a timber panic; and 

'Gaetano Rossi of Catanzaro. This was the libretto writer 
(1772-1855), and hence the imperfections of the work can better be 
condoned. De Morgan should have given a little more of the title: 
Soluzione esatta e regolare .... del .... problema della quadratura 
del circolo. There was a second edition, London, 1805. 

8 This identifies Rossi, for Josephine Grassini (1773-1850) was 
a well-known contralto, prima donna at Napoleon's court opera. 

/William Spence (1783-1860) was an entomologist and econ- 
omist of some standing, a fellow of the Royal Society, and one of 
the founders of the Entomological Society of London. The work 
here mentioned was a popular one, the first edition appearing in 
1807, and four editions being justified in a single year. He also 
wrote Agriculture the Source of Britain's Wealth (1808) and Ob- 
jections against the Corn Bill refuted (1815), besides a work in four 
volumes on entomology (1815-1826) in collaboration with William 
Kirby. 



232 A BUDGET OF PARADOXES. 

a solemn embassy to the Americans, to beg them not to 
whittle, would be desirable. There was a gold panic be- 
ginning, before the new fields were discovered. For myself, 
I am the unknown and unpitied victim of a chronic gutta- 
percha panic : I never could get on without it ; to me, gutta 
percha and Rowland Hill are the great discoveries of our 
day; and not unconnected either, gutta percha being to the 
submarine post what Rowland Hill is to the superterrene. 
I should be sorry to lose cow-choke I gave up trying to 
spell it many years ago but if gutta percha go, I go too. 
I think, that perhaps when, five hundred years hence, the 
people say to the Brit. Assoc. (if it then exist) "Pray gentle- 
men, is it not time for the coal to be exhausted?" they will 
be answered out of Moliere (who will certainly then exist) : 
"Cela etait autrefois ainsi, mais nous avons change tout 
cela." z A great many people think that if the coal be used 
up, it will be announced some unexpected morning by all 
the yards being shut up and written notice outside, "Coal 
all gone !" just like the "Please, ma'am, there ain't no more 
sugar," with which the maid servant damps her mistress 
just at breakfast-time. But these persons should be informed 
that there is every reason to think that there will be time, 
as the city gentleman said, to venienti the occurrite morbo. 3 

SOME SCIENTIFIC PARADOXES. 

An appeal to the republic of letters in behalf of injured science, 
from the opinions and proceedings of some modern authors 
of elements of geometry. By George Douglas. 1 Edinburgh, 
1810, 8vo. 

Mr. Douglas was the author of a very good set of mathe- 

3 "That used to be so, but we have changed all that." 
8 "Meet the coming disease." 

1 George Douglas (or Douglass) was a Scotch writer. He got 
out an edition of the Elements of Euclid in 1776, with an appendix 
on trigonometry and a set of tables. His work on Mathematical 
Tables appeared in 1809, and his Art of Drawing in Perspective, 
from mathematical principles, in 1810. 



SOME SCIENTIFIC PARADOXES. 233 

matical tables, and of other works. He criticizes Simson, 2 
Playfair, 3 and others, sometimes, I think, very justly. 
There is a curious phrase which occurs more than once. 
When he wants to say that something or other was done 
before Simson or another was born, he says "before he 
existed, at least as an author." He seems to reserve the 
possibility of Simson's pre-existence, but at the same time 
to assume that he never wrote anything in his previous 
state. Tell me that Simson pre-existed in any other way 
than as editor of some pre-existent Euclid? Tell Apella! 4 
1810. In this year Jean Wood, Professor of Mathemat- 
ics in the University of Virginia (Richmond), 5 addressed 
a printed circular to "Dr. Herschel, Astronomer, Greenwich 
Observatory." No mistake was more common than the 
natural one of imagining that the Private Astronomer of the 
king was the Astronomer Royal The letter was on the 

8 See note 3, on page 197. 

'John Playfair (1748-1848) was professor of mathematics (1785) 
and natural philosophy (1805) at the University of Edinburgh. His 
Elements of Geometry went through many editions. 

'"Tell Apella" was an expression current in classical Rome to 
indicate incredulity and to show the contempt in which the Jew was 
held. Horace says: Credat Judaus Apella, "Let Apella the Jew be- 
lieve it." Our "Tell it to the marines," is a similar phrase. 

5 As De Morgan says two lines later, "No mistake is more com- 
mon than the natural one of imagining that the" University of Vir- 
ginia is at Richmond. The fact is that it is not there, and that it 
did not exist in 1810. It was not chartered until 1819, and was not 
opened until 1825, and then at Charlottesville. The act establishing 
the Central College, from which the University of Virginia devel- 
oped, was passed in 1816. The Jean Wood to whom De Morgan 
refers was one John Wood who was born about 1775 in Scotland 
and who emigrated to the United States in 1800. He published a 
History of the Administration of J. Adams (New York, 1802) that 
was suppressed by Aaron Burr. This act called forth two works, 
a Narrative of the Suppression, by Col Burr, of the 'History of the 
Administration of John Adams' (1802), in which Wood was sus- 
tained; and the Antidote to John Wood's Poison (1802), in which 
he was attacked. The work referred to in the "printed circular" 
may have been the New theory of the diurnal rotation of the earth 
^Richmond, Va., 1809). Wood spent the last years of his life in 
Richmond, Va., making county maps. He died there in 1822. A 
careful search through works relating to the University of Virginia 
fails to show that Wood had any connection with it. 



234 A BUDGET OF PARADOXES. 

difference of velocities of the two sides of the earth, arising 
from the composition of the rotation and the orbital motion. 
The paradox is a fair one, and deserving of investigation; 
but, perhaps it would not be easy to deduce from it tides, 
trade-winds, aerolithes, &c., as Mr. Wood thought he had 
done in a work from which he gives an extract, and which 
he describes as published. The composition of rotations, 
&c., is not for the world at large: the paradox of the non- 
rotation of the moon about her axis is an instance. Ht>w 
many persons know that when a wheel rolls on the ground, 
the lowest point is moving upwards, the highest point for- 
wards, and the intermediate points in all degrees of betwixt 
and between? This is too short an explanation, with some 
good difficulties. 

The Elements of Geometry. In 2 vols. [By the Rev. J. Dob- 
son, 6 B.D.] Cambridge, 1815. 4to. 

Of this unpunctuating paradoxer I shall give an account 
in his own way : he would not stop for any one ; why should 
I stop for him ? It is worth while to try how unpunctuated 
sentences will read. 

The reverend J Dobson BD late fellow of saint Johns 
college Cambridge was rector of Brandesburton in York- 
shire he was seventh wrangler in 1798 and died in 1847 he 
was of that sort of eccentricity which permits account of his 
private life if we may not rather say that in such cases 
private life becomes public there is a tradition that he was 
called Death Dobson on account of his head and aspect of 
countenance being not very unlike the ordinary pictures of 
a human skull his mode of life is reported to have been very 
singular whenever he visited Cambridge he was never known 
to go twice to the same inn he never would sleep at the 
rectory with another person in the house some ancient char- 
woman used to attend to the house but never slept in it he 
has been known in the time of coach travelling to have de- 

6 There seems to be nothing to add to Dobson's biography beyond 
what De Morgan has so deliciously set forth. 



SOME SCIENTIFIC PARADOXES. 235 

ferred his return to Yorkshire on account of his disinclina- 
tion to travel with a lady in the coach he continued his 
mathematical studies until his death and till his executors 
sold the type all his tracts to the number of five were kept in 
type at the university press none of these tracts had any 
stops except full stops at the end of paragraphs only neither 
had they capitals except one at the beginning of a paragraph 
so that a full stop was generally followed by some white 
as there is not a single proper name in the whole of the 
book I have I am not able to say whether he would have used 
capitals before proper names I have inserted them as usual 
for which I hope his spirit will forgive me if I be wrong he 
also published the elements of geometry in two volumes 
quarto Cambridge 1815 this book had also no stops except 
when a comma was wanted between letters as in the straight 
lines AB, BC I should also say that though the title is un- 
punctuated in the author's part it seems the publishers would 
not stand it in their imprint this imprint is punctuated as 
usual and Deighton and Sons to prove the completeness of 
their allegiance have managed that comma semicolon and 
period shall all appear in it why could they not have con- 
trived interrogation and exclamation this is a good precedent 
to establish the separate right of the publisher over the 
imprint it is said that only twenty of the tracts were printed 
and very few indeed of the book on geometry it is doubtful 
whether any were sold there is a copy of the geometry in 
the university library at Cambridge and I have one myself 
the matter of the geometry differs entirely from Euclid and 
is so fearfully prolix that I am sure no mortal except the 
author ever read it the man went on without stops and with- 
out stop save for a period at the end of a paragraph this is 
the unpunctuated account of the unpunctuating geometer 
suum cuique tribuito 7 Mrs Thrale 8 would have been amused 

7 "Give to each man his due." 

8 Hester Lynch Salusbury (1741-1821), the friend of Dr. John- 
son, married Henry Thrale (1763), a brewer, who died in 1781. 
She then married Gabriel Piozzi (1784), an Italian musician. Her 



236 A BUDGET OF PARADOXES. 

at a Dobson who managed to come to a full stop without 
either of the three warnings. 

I do not find any difficulty in reading Dobson's geom- 
etry; and I have read more of it to try reading without 
stops than I should have done had it been printed in the 
usual way. Those who dip into the middle of my paragraph 
may be surprised for a moment to see "on account of his 
disinclination to travel with a lady in the coach he continued 
his mathematical studies until his death and [further, of 
course] until his executors sold the type." But a person 
reading straight through would hardly take it so. I should 
add that, in order to give a fair trial, I did not compose as 
I wrote, but copied the words of the correspondent who gave 
me the facts, so far as they went. 

A RELIGIOUS PARADOX. 

Philosophia Sacra, or the principles of natural Philosophy. Ex- 
tracted from Divine Revelation. By the Rev. Samuel Pike. 1 
Edited by the Rev. Samuel Kittle. 2 Edinburgh, 1815, 8vo. 

This is a work of modified Hutchinsonianism, which I 
have seen cited by several. Though rather dark on the sub- 
ject, it seems not to contradict the motion of the earth, or 
the doctrine of gravitation. Mr. Kittle gives a list of some 
Hutchinsonians, as Bishop Home ; 3 Dr. Stukeley ; 4 the Rev. 

Anecdotes of the late Samuel Johnson (1786) and Letters to and 
from Samuel Johnson (1788) are well known. She also wrote 
numerous essays and poems. 

1 Samuel Pike (c. 1717-1773) was an independent minister, with 
a chapel in London and a theological school in his house. He later 
became a disciple of Robert Sandeman and left the Independents 
for the Sandemanian church (1765). The Philosophia Sacra was 
first published at London in 1753. De Morgan here cites the second 
edition. 

* Pike had been dead over forty years when Kittle published this 
second edition. Kittle had already published a couple of works : 
King Solomon's portraiture of Old Age (Edinburgh, 1813), and 
Critical and Practical Lectures on the Apocalyptical Epistles to the 
Seven Churches of Asia Minor (London, 1814). 

8 See note i, on page 152. 

4 William Stukely (1687-1765) was a fellow of the Royal Society 
and of the College of Physicians and Surgeons. He afterwards 



A RELIGIOUS PARADOX. 237 

W. Jones, 5 author of Physiological Disquisitions ; Mr. Spear- 
man, 6 author of Letters on the Septuagint and editor of 
Hutchinson ; Mr. Barker, 7 author of Reflexions on Learn- 
ing ; Dr. Catcott, 8 author of a work on the creation, &c. ; Dr. 
Robertson, 9 author of a Treatise on the Hebrew Language ; 
Dr. Holloway, 10 author of Originals, Physical and Theolog- 
ical ; Dr. Walter Hodges, 11 author of a work on Elohim ; 
Lord President Forbes (ob. 1747). ia 

The Rev. William Jones, above mentioned (1726-1800), 
the friend and biographer of Bishop Home and his stout 

(1729) entered the Church. He was prominent as an antiquary, 
especially in the study of the Roman and Druidic remains of Great 
Britain. He was the author of numerous works, chiefly on paleog- 
raphy. 

5 William Jones (1726-1800), who should not be confused with 
his namesake who is mentioned in note 3 on page 135. He was a 
lifelong friend of Bishop Horne, and his vicarage at Nayland was 
a meeting place of an influential group of High Churchmen. Be- 
sides the Physiological Disquisitions (1781) he wrote The Catholic 
Doctrine of the Trinity (1756) and The Grand Analogy (1793). 

'Robert Spearman (1703-1761) was a pupil of John Hutchin- 
son, and not only edited his works but wrote his life. He wrote a 
work against the Newtonian physics, entitled An Enquiry after Phi- 
losophy and Theology (Edinburgh, 1755), besides the Letters to a 
Friend concerning the Septuagint Translation (Edinburgh, 1759) to 
which De Morgan refers. 

T A writer of no importance, at least in the minds of British 
biographers. 

"Alexander Catcott (1725-1779), a theologian and geologist, 
wrote not only a work on the creation (1756) but a Treatise on the 
Deluge (1761, with a second edition in 1768). Sir Charles Lyell 
considered the latter work a valuable contribution to geology. 

8 James Robertson (1714-1795), professor of Hebrew at the Uni- 
versity of Edinburgh. Probably De Morgan refers to his Grarn- 
matica Linguae Hebraa (Edinburgh, 1758; with a second edition in 
1783). He also wrote Clavis Pentateuchi (1770). 

"Benjamin Holloway (c. 1691-1759), a geologist and theologian. 
He translated Woodward's Naturalis Historia Telluris, and was in- 
troduced by Woodward to Hutchinson. The work referred to by 
De Morgan appeared at Oxford in two volumes in 1754. 

" His work was The Christian plan exhibited in the interpretation 
of Elohim: with observations upon a few other matters relative to 
the same subject, Oxford, 1752, with a second edition in 1755. 

"Duncan Forbes (1685-1747) studied Oriental languages and 
civil law at Leyden. He was Lord President of the Court of Ses- 
sions (i737). He wrote a number of theological works. 



238 A BUDGET OF PARADOXES. 

defender, is best known as William Jones of Nayland, who 
(1757) 13 published the Catholic Doctrine of the Trinity; he 
was also strong for the Hutchinsonian physical trinity of 
fire, light, and spirit. This well-known work was generally 
recommended, as the defence of the orthodox system, to 
those who could not go into the learning of the subject. 
There is now a work more suited to our time : The Rock of 
Ages, by the Rev. E. H. Bickersteth, 14 now published by 
the Religious Tract Society, without date, answered by the 
Rev. Dr. Sadler, 15 in a work (1859) entitled Gloria Patri, 
in which, says Mr. Bickersteth, "the author has not even 
attempted to grapple with my main propositions." I have 
read largely on the controversy, and I think I know what 
this means. Moreover, when I see the note "There are two 
other passages to which Unitarians sometimes refer, but the 
deduction they draw from them is, in each case, refuted by 
the context" I think I see why the two texts are not named. 
Nevertheless, the author is a little more disposed to yield to 
criticism than his foregoers ; he does not insist on texts and 
readings which the greatest editors have rejected. And he 
writes with courtesy, both direct and oblique, towards his 
antagonists ; which, on his side of this subject, is like letting 
in fresh air. So that I suspect the two books will together 
make a tolerably good introduction to the subject for those 
who cannot go deep. Mr. Bickersteth's book is well arranged 
and indexed, which is a point of superiority to Jones of 
Nayland. There is a point which I should gravely recom- 
mend to writers on the orthodox side. The Unitarians in 

13 Should be 1756. 

"Edward Henry Bickersteth (1825-1906), bishop of Exeter 
(1885-1900) ; published The Rock of Ages; or scripture testimony to 
the one Eternal Godhead of the Father, and of the Son, and of the 
Holy Ghost at Hampstead in 1859. A second edition appeared at 
London in 1860. 

"Thomas Sadler (1822-1891) took his Ph.D. at Erlangen in 
1844, and became a Unitarian minister at Hampstead, where Bicker- 
steth's work was published. Besides writing the Gloria Patri (1859), 
he edited Crabb Robinson's Diaries. 



A RELIGIOUS PARADOX. 239 

England have frequently contended that the method of prov- 
ing the divinity of Jesus Christ from the New Testament 
would equally prove the divinity of Moses. I have not fallen 
in the way of any orthodox answers specially directed at the 
repeated tracts written by Unitarians in proof of their asser- 
tion. If there be any, they should be more known ; if there 
be none, some should be written. Which ever side may 
be right, the treatment of this point would be indeed com- 
ing to close quarters. The heterodox assertion was first 
supported, it is said, by John Bidle or Biddle (1615-1662) 
of Magdalen College, Oxford, the earliest of the English 
Unitarian writers, previously known by a translation of 
part of Virgil and part of Juvenal. 16 But I cannot find that 
he wrote on it. 17 It is the subject of "alptcrew dvao-rao-ts, or 
a new way of deciding old controversies. By Basanistes. 
Third edition, enlarged," London, 1815, 8vo. 18 It is the 
appendix to the amusing, "Six more letters to Granville 
Sharp, Esq., ... By Gregory Blunt, Esq." London, 8vo., 
1803. 19 This much I can confidently say, that the study of 
these tracts would prevent orthodox writers from some 
curious slips, which are slips obvious to all sides of opinion. 
The lower defenders of orthodoxy frequently vex the spirits 
of the higher ones. 

Since writing the above I have procured Dr. Sadler's 
answer. I thought I knew what the challenger meant 
when he said the respondent had not grappled with his main 

"This was his Virgil's Bucolics and the two first Satyrs of 
Juvenal, 1634. 

17 Possibly in his Twelve Questions or Arguments drawn out of 
Scripture, wherein the commonly received Opinion touching the 
Deity of the Holy Spirit is clearly and fully refuted, 1647. This was 
his first heretical work, and it was followed by a number of others 
that were written during the intervals in which the Puritan parlia- 
ment allowed him out of prison. It was burned by the hangman as 
blasphemous. Biddle finally died in prison, unrepentant to the last. 

"The first edition of the anonynous 'Atpeffewv dvaa-raffts (by 
Vicars?) appeared in 1805. 

"^Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. 
Peter's College, Cambridge, and a Unitarian minister. 



240 A BUDGET OF PARADOXES. 

propositions. I should say that he is clung on to from be- 
ginning to end. But perhaps Mr. B. has his own meaning 
of logical terms, such as "proposition" : he certainly has his 
own meaning of "cumulative." He says his evidence is 
cumulative; not a catena, the strength of which is in its 
weakest part, but distinct and independent lines, each of 
which corroborates the other. This is the very opposite of 
cumulative: it is distributive. When different arguments 
are each necessary to a conclusion, the evidence is cumu- 
lative ; when any one will do, even though they strengthen 
each other, it is distributive. The word "cumulative" is a 
synonym of the law word "constructive"; a whole which 
will do made out of parts which separately will not. Lord 
Strafford 20 opens his defence with the use of both words: 
"They have invented a kind of accumulated or constructive 
evidence ; by which many actions, either totally innocent in 
themselves, or criminal in a much inferior degree, shall, 
when united, amount to treason." The conclusion is, that 
Mr. B. is a Cambridge man; the Oxford men do not con- 
fuse the elementary terms of logic. O dear old Cambridge ! 
when the New Zealander comes let him find among the 
relics of your later sons some proof of attention to the 
elementary laws of thought. A little-go of logic, please! 
Mr. B., though apparently not a Hutchinsonian, has 
a nibble at a physical Trinity. "If, as we gaze on the sun 
shining in the firmament, we see any faint adumbration of 
the doctrine of the Trinity in the fontal orb, the light ever 
generated, and the heat proceeding from the sun and its 
beams threefold and yet one, the sun, its light, and its 

20 Thomas Wentworth, Earl of Strafford, was borne in London 
in 1593, and was executed there in 1641. He was privy councilor to 
Charles I, and was Lord Deputy of Ireland. On account of his 
repressive measures to uphold the absolute power of the king he 
was impeached by the Long Parliament and was executed for trea- 
son. The essence of his defence is in the sentence quoted by De 
Morgan, to which Pym replied that taken as a whole, the acts tended 
to show an intention to change the government, and this was in 
itself treason. 



A RELIGIOUS PARADOX. 241 

heat, that luminous globe, and the radiance ever flowing 
from it, are both evident to the eye; but the vital warmth 
is felt, not seen, and is only manifested in the life it trans- 
fuses through creation. The proof of its real existence is 
self-demonstrating." 

We shall see how Revilo 21 illustrates orthodoxy by mathe- 
matics. It was my duty to have found one of the many 
illustrations from physics; but perhaps I should have for- 
gotten it if this instance had not come in my way. It is 
very bad physics. The sun, apart from its light, evident 
to the eyel Heat more self-demonstrating than light, be- 
cause felt I Heat only manifested by the life it diffuses! 
Light implied not necessary to life! But the theology is 
worse than Sabellianism. 22 To adumbrate i. e., make a 
picture of the orthodox doctrine, the sun must be heavenly 
body, the light heavenly body, the heat heavenly body ; and 
yet, not three heavenly bodies, but one heavenly body. The 
truth is, that this illustration and many others most strik- 
ingly illustrate the Trinity of fundamental doctrine held by 
the Unitarians, in all its differences from the Trinity of 
persons held by the Orthodox. Be right which may, the 
right or wrong of the Unitarians shines out in the compari- 
son. Dr. Sadler confirms me by which I mean that I wrote 
the above before I saw what he says in the following 
words : "The sun is one object with two properties, and these 
properties have a parallel not in the second and third per- 
sons of the Trinity, but in the attributes of Deity." 

The letting light alone, as self-evident, and making heat 
self-demonstrating, because felt i. e., perceptible now and 
then has the character of the Irishman's astronomy: 

81 The name assumed by a writer who professed to give a mathe- 
matical explanation of the Trinity, see farther on. S. E. De M. 

"Sabellius (fl. 230 A. D.) was an early Christian of Libyan 
origin. He taught that Father, Son, and Holy Spirit were different 
names for the same person. 



242 A BUDGET OF PARADOXES. 

"Long life to the moon, for a dear noble cratur, 
Which serves us for lamplight all night in the dark, 
While the sun only shines in the day, which by natur, 
Wants no light at all, as ye all may remark." 

SIR RICHARD PHILLIPS. 

Sir Richard Phillips* (born 1768) was conspicuous in 
1793, when he was sentenced to a year's imprisonment 2 for 
selling Paine's Rights of Man ; and again when, in 1807, 3 
he was knighted as Sheriff of London. As a bookseller, 
he was able to enforce his opinions in more ways than 
others. For instance, in James Mitchell's 4 Dictionary of the 
Mathematical and Physical Sciences, 1823, 12mo, which, 
though he was not technically a publisher, was printed for 
him a book I should recommend to the collector of works 
of reference there is a temperate description of his doc- 
trines, which one may almost swear was one of his condi- 
tions previous to undertaking the work. Phillips himself 
was not only an anti-Newtonian, but carried to a fearful 
excess the notion that statesmen and Newtonians were in 
league to deceive the world. He saw this plot in Mrs. 
Airy's 5 pension, and in Mrs. Somerville's. 6 In 1836, he 

1 Sir Richard Phillips was born in London in 1767 (not 1768 as 
stated above), and died there in 1840. He was a bookseller and 
printer in Leicester, where he also edited a radical newspaper. He 
went to London to live in 1795 and started the Monthly Magazine 
there in 1796. Besides the works mentioned by De Morgan he wrote 
on law and economics. 

a lt was really eighteen months. 

8 While he was made sheriff in 1807 he was not knighted until 
the following year. 

4 James Mitchell (c. 1786-1844) was a London actuary, or 
rather a Scotch actuary living a good part of his life in London. 
Besides the work mentioned he compiled a Dictionary of Chemistry, 
Mineralogy, and Geology (1823), and wrote On the Plurality of 
Worlds (1813) and The Elements of Astronomy (1820). 

5 Richarda Smith, wife of Sir George Biddell Airy (see note 2, 
page 85) the astronomer. In 1835 Sir Robert Peel offered a pension 
of ^300 a year to Airy, who requested that it be settled on his wife. 

"Mary Fairfax (1780-1872) married as her second husband Dr. 
William Somerville. In 1826 she presented to the Royal Society a 



SIR RICHARD PHILLIPS. 243 

did me the honor to attempt my conversion. In his first 
letter he says: 

"Sir Richard Phillips has an inveterate abhorrence of 
all the pretended wisdom of philosophy derived from the' 
monks and doctors of the middle ages, and not less of those 
of higher name who merely sought to make the monkish 
philosophy more plausible, or so to disguise it as to mystify 
the mob of small thinkers." 

So little did his writings show any knowledge of an- 
tiquity, that I strongly suspect, if required to name one of 
the monkish doctors, he would have answered Aristotle. 
These schoolmen, and the "philosophical trinity of gravi- 
tating force, projectile force, and void space," were the 
bogies of his life. 

I think he began to publish speculations in the Monthly 
Magazine (of which he was editor) in July 1817: these he 
republished separately in 1818. In the Preface, perhaps 
judging the feelings of others by his own, he says that he 
"fully expects to be vilified, reviled, and anathematized, for 
many years to come." Poor man! he was let alone. He 
appeals with confidence to the "impartial decision of pos- 
terity"; but posterity does not appoint a hearing for one 
per cent, of the appeals which are made ; and it is much to 
be feared that an article in such a work of reference as this 
will furnish nearly all her materials fifty years hence. The 
following, addressed to M. Arago, 7 in 1835, will give pos- 
terity as good a notion as she will probably need: 

"Even the present year has afforded EVER-MEMORABLE 
examples, paralleled only by that of the Romish Conclave 
which persecuted Galileo. Policy has adopted that maxim of 
Machiavel which teaches that it is more prudent to reward 

paper on The Magnetic Properties of the Violet Rays of the Solar 
Spectrum, which attracted much attention. It was for her Mechan- 
ism of the Heavens (1831), a popular translation of Laplace's Meca- 
nique Celeste, that she was pensioned. 

7 Dominique Frangois Jean Arago (1786-1853) the celebrated 
French astronomer and physicist. 



244 A BUDGET OF PARADOXES. 

partisans than to persecute opponents. Hence, a bigotted 
party had influence enough with the late short-lived adminis- 
tration [I think he is wrong as to the administration] of 
Wellington, Peel, &c., to confer munificent royal pensions on 
three writers whose sole distinction was their advocacy of 
the Newtonian philosophy. A Cambridge professor last year 
published an elaborate volume in illustration of Gravitation, 
and on him has been conferred a pension of 300/. per annum. 
A lady has written a light popular view of the Newtonian 
Dogmas, and she has been complimented by a pension of 
2001. per annum. And another writer, who has recently 
published a volume to prove that the only true philosophy is 
that of Moses, has been endowed with a pension of 200/. 
per annum. Neither of them were needy persons, and the 
political and ecclesiastical bearing of the whole was indicated 
by another pension of 300/. bestowed on a political writer, 
the advocate of all abuses and prejudices. Whether the con- 
duct of the Romish Conclave was more base for visiting with 
legal penalties the promulgation of the doctrines that the 
Earth turns on its axis and revolves around the Sun ; or that 
of the British Court, for its craft in conferring pensions on 
the opponents of the plain corollary, that all the motions of 
the Earth are 'part and parcel' of these great motions, and 
those again and all like them consecutive displays of still 
greater motions in equality of action and reaction, is A QUES- 
TION which must be reserved for the casuists of other genera- 
tions .... I cannot expect that on a sudden you and your 
friends will come to my conclusion, that the present philos- 
ophy of the Schools and Universities of Europe, based on 
faith in witchcraft, magic, &c., is a system of execrable 
nonsense, by which quacks live on the faith of fools ; but I 
desire a free and fair examination of my Aphorisms, and if 
a few are admitted to be true, merely as courteous con- 
cessions to arithmetic, my purpose will be effected, for men 
will thus be led to think ; and if they think, then the fabric 



SIR RICHARD PHILLIPS. 245 

of false assumptions, and degrading superstitions will soon 
tumble in ruins." 

This for posterity. For the present time I ground the 
fame of Sir R. Phillips on his having squared the circle 
without knowing it, or intending to do it. In the Protest 
presently noted he discovered that "the force taken as 1 is 
equal to the sum of all its fractions. . .thus 1 = % + % + %6 
+ %s> & c -> carried to infinity." This the mathematician in- 
stantly sees is equivalent to the theorem that the circum- 
ference of any circle is double of the diagonal of the cube 
on its diameter. 8 

I have examined the following works of Sir R. Phillips, 
and heard of many others : 

Essays on the proximate mechanical causes of the general phe- 

nomena of the Universe, 1818, I2mo. 9 
Protest against the prevailing principles of natural philosophy, 

with the development of a common sense system (no date, 

8vo, pp. i6). 10 
Four dialogues between an Oxford Tutor and a disciple of the 

common-sense philosophy, relative to the proximate causes of 

material phenomena. 8vo, 1824. 
A century of original aphorisms on the proximate causes of the 

phenomena of nature, 1835, I2mo. 

Sir Richard Phillips had four valuable qualities ; honesty, 
zeal, ability, and courage. He applied them all to teaching 



8 For there is a well-known series 

t- -22+3*4- . . . = -g-. 
If, therefore, the given series equals I, we hav 



or 7r s = l2, 
whence IT = 2]/37 

But c = itd, and twice the diagonal of a cube on the diameter 
is 2dV^T 

"There was a second edition in 1821. 
"London, 1830. 



246 A BUDGET OF PARADOXES. 

matters about which he knew nothing; and gained himself 
an uncomfortable life and a ridiculous memory. 

Astronomy made plain; or only way the true perpendicular dis- 
tance of the Sun, Moon, or Stars, from this earth, can be ob- 
tained. By Wm. Wood. 11 Chatham, 1819, I2mo. 

If this theory be true, it will follow, of course, that this 
earth is the only one God made, and that it does not whirl 
round the sun, but vice versa, the sun round it. 



WHATELY'S FAMOUS PARADOX. 

Historic doubts relative to Napoleon Buonaparte. London, 1819, 
8vo. 

This tract has since been acknowledged by Archbishop 
Whately 1 and reprinted. It is certainly a paradox: but dif- 
fers from most of those in my list as being a joke, and a 
satire upon the reasoning of those who cannot receive nar- 
rative, no matter what the evidence, which is to them utterly 
improbable a priori. But had it been serious earnest, it 
would not have been so absurd as many of those which I 
have brought forward. The next on the list is not a joke. 

The idea of the satire is not new. Dr. King, 2 in the 
dispute on the genuineness of Phalaris, proved with humor 
that Bentley did not write his own dissertation. An attempt 
has lately been made, for the honor of Moses, to prove, 

"He was a resident of Chatham, and seems to have published 
no other works. 

^Richard Whately (1787-1863) was, as a child, a calculating 
prodigy (see note 3, page 86), but lost the power as is usually the 
case with well-balanced minds. He was a fellow of Oriel College, 
Oxford, and in 1825 became principal of St. Alban Hall. He was 
a friend of Newman, Keble, and others who were interested in the 
religious questions of the day. He became archbishop of Dublin in 
1831. He was for a long time known to students through his Logic 
(1826) and Rhetoric (1828). 

3 William King, D.C.L. (1663-1712), student at Christ Church, 
Oxford, and celebrated as a wit and scholar. His Dialogues of the 
Dead (1699) is a satirical attack on Bentley. 



WHATELY'S FAMOUS PARADOX. 247 

without humor, that Bishop Colenso did not write his own 
book. This is intolerable: anybody who tries to use such a 
weapon without banter, plenty and good, and of form suited 
to the subject, should get the drubbing which the poor man 
got in the Oriental tale for striking the dervishes with the 
wrong hand. 

The excellent and distinguished author of this tract has 
ceased to live. I call him the Paley of our day : with more 
learning and more purpose than his predecessor; but per- 
haps they might have changed places if they had changed 
centuries. The clever satire above named is not the only 
work which he published without his name. The following 
was attributed to him, I believe rightly: "Considerations 
on the Law of Libel, as relating to Publications on the 
subject of Religion, by John Search." London, 1833, 8vo. 
This tract excited little attention: for those who should 
have answered, could not. Moreover, it wanted a prosecu- 
tion to call attention to it : the fear of calling such attention 
may have prevented prosecutions. Those who have read 
it will have seen why. 

The theological review elsewhere mentioned attributes 
the pamphlet of John Search on blasphemous libel to Lord 
Brougham. This is quite absurd: the writer states points 
of law on credence where the judge must have spoken with 
authority. Besides which, a hundred points of style are 
decisive between the two. I think any one who knows 
Whately's writing will soon arrive at my conclusion. Lord 
Brougham himself informs me that he has no knowledge 
whatever of the pamphlet. 

It is stated in Notes and Queries (3 S. xi. 511) that 
Search was answered by the Bishop of Ferns 3 as S. N., with 

8 Thomas Ebrington (1760-1835) was a fellow of Trinity College, 
Dublin, and taught divinity, mathematics, and natural philosophy 
there. He became provost of the college in 1811, bishop of Lim- 
erick in 1820, and bishop of Leighlin and Ferns in 1822. His edition 
of Euclid was reprinted a dozen times. The Reply to John Search's 
Considerations on the Law of Libel appeared at Dublin in 1834. 



248 A BUDGET OF PARADOXES. 

a rejoinder by Blanco White. 4 These circumstances increase 
the probability that Whately was written against and for. 

VOLTAIRE A CHRISTIAN. 

Voltaire Chretien; preuves tirees de ses ouvrages. Paris, 1820, 
I2mo. 

If Voltaire have not succeeded in proving himself a 
strong theist and a strong anti-revelationist, who is to suc- 
ceed in proving himself one thing or the other in any matter 
whatsoever? By occasional confusion between theism and 
Christianity ; by taking advantage of the formal phrases of 
adhesion to the Roman Church, which very often occur, and 
are often the happiest bits of irony in an ironical produc- 
tion ; by citations of his morality, which is decidedly Chris- 
tian, though often attributed to Brahmins; and so on 
the author makes a fair case for his paradox, in the eyes 
of those who know no more than he tells them. If he had 
said that Voltaire was a better Christian than himself knew 
of, towards all mankind except men of letters, I for one 
should have agreed with him. 

Christian! the word has degenerated into a synonym of 
man, in what are called Christian countries. So we have 
the parrot who "swore for all the world like a Christian," 
and the two dogs who "hated each other just like Chris- 
tians." When the Irish duellist of the last century, whose 
name may be spared in consideration of its historic fame 

* Joseph Blanco White (1775-1841) was the son of an Irishman 
living in Spain. He was born at Seville and studied for orders 
there, being ordained priest in 1800. He lost his faith in the Roman 
Catholic Church, and gave up the ministry, escaping to England at 
the time of the French invasion. At London he edited Espanol, a 
patriotic journal extensively circulated in Spain, and for this service 
he was pensioned after the expulsion of the French. He then studied 
at Oriel College, Oxford, and became intimate with men like Whately, 
Newman, and Keble. In 1835 he became a Unitarian. Among his 
theological writings is his Evidences against Catholicism (1825). The 
"rejoinder" to which De Morgan refers consisted of two letters : 
The law of anti-religious Libel reconsidered (Dublin, 1834) and An 
Answer to some Friendly Remarks on "The Law of Anti-Religious 
Libel Reconsidered" (Dublin, 1834). 



WRONSKI ON THE LONGITUDE PROBLEM. 249 

and the worthy people who bear it, was (June 12, 1786) 
about to take the consequence of his last brutal murder, 
the rope broke, and the criminal got up, and exclaimed, 
"By - - Mr. Sheriff, you ought to be ashamed of your- 
self ! this rope is not strong enough to hang a dog, far less 
a Christian!" But such things as this are far from the 
worst depravations. As to a word so defiled by usage, it 
is well to know that there is a way of escape from it, with- 
out renouncing the New Testament. I suppose any one 
may assume for himself what I have sometimes heard con- 
tended for, that no New Testament word is to be used in 
religion in any sense except that of the New Testament. 
This granted, the question is settled. The word Christian, 
which occurs three times, is never recognized as anything 
but a term of contempt from those without the pale to 
those within. Thus, Herod Agrippa, who was deep in 
Jewish literature, and a correspondent of Josephus, says to 
Paul (Acts xxvi. 28), "Almost thou persuadest me to be 
(what I and other followers of the state religion despise 
under the name) a Christian." Again (Acts xi. 26), "The 
disciples (as they called themselves) were called (by the 
surrounding heathens) Christians first in Antioch." Thirdly 
(1 Peter iv. 16), "Let none of you suffer as a murderer. . . . 
But if as a Christian (as the heathen call it by whom the 
suffering conies), let him not be ashamed." That is to 
say, no disciple ever called himself a Christian, or applied 
the name, as from himself, to another disciple, from one 
end of the New Testament to the other; and no disciple 
need apply that name to himself in our day, if he dislike 
the associations with which the conduct of Christians has 
clothed it. 

WRONSKI ON THE LONGITUDE PROBLEM. 

Address of M. Hoene Wronski to the British Board of Longi- 
tude, upon the actual state of the mathematics, their reform, 



250 A BUDGET OF PARADOXES. 

and upon the new celestial mechanics, giving the definitive solu- 
tion of the problem of longitude. 1 London, 1820, 8vo. 

M. Wronski 2 was the author of seven quartos on mathe- 
matics, showing very great power of generalization. He 
was also deep in the transcendental philosophy, 3 and had 
the Absolute at his fingers' ends. All this knowledge was 
rendered useless by a persuasion that he had greatly ad- 
vanced beyond the whole world, with many hints that the 
Absolute would not be forthcoming, unless prepaid. He 
was a man of the widest extremes. At one time he desired 
people to see all possible mathematics in 

Rr = A O + A^ + A 2 O 2 + A 3 O 3 + &c. 

which he did not explain, though there is meaning to it in 
the quartos. At another time he was proposing the general 
solution of the 4 fifth degree by help of 625 independent 
equations of one form and 125 of another. The first sep- 
arate memoir from any Transactions that I ever possessed 
was given to me when at Cambridge ; the refutation (1819) 
of this asserted solution, presented to the Academy of Lis- 
bon by Evangelista Torriano. I cannot say I read it. The 
tract above is an attack on modern mathematicians in gen- 
eral, and on the Board of Longitude, and Dr. Young. 5 

a The work was translated from the French. 

3 J. Hoe'ne Wronski (1778-1853) served, while yet a mere boy, 
as an artillery officer in Kosciusko's army (1791-1794). He was 
imprisoned after the battle of Maciejowice. He afterwards lived in 
Germany, and (after 1810) in Paris. For the bibliography of his 
works see S. Dickstein's article in the Bibliotheca Mathematics, vol. 
VI (2), page 48. 

3 Perhaps referring to his Introduction a la philosophic des 
mathematiques (1811). 

4 Read "equation of the." 

5 Thomas Young (1773-1829), physician and physicist, some- 
times called the founder of physiological optics. He seems to have 
initiated the theory of color blindness that was later developed by 
Helmholtz. The attack referred to was because of his connection 
with the Board of Longitude, he having been made (1818) super- 
intendent of the Nautical Almanac and secretary of the Board. He 
opposed introducing into the Nautical Almanac anything not imme- 
diately useful to navigation, and this antagonized many scientists. 



DR. MILNER'S PARADOXES. 251 

DR. MILNER'S PARADOXES. 

1820. In this year died Dr. Isaac Milner, 1 President of 
Queens' College, Cambridge, one of the class of rational 
paradoxers. Under this name I include all who, in private 
life, and in matters which concern themselves, take their 
own course, and suit their own notions, no matter what 
other people may think of them. These men will put things 
to uses they were never intended for, to the great distress 
and disgust of their gregarious friends. I am one of the 
class, and I could write a little book of cases in which I 
have incurred absolute reproach for not "doing as other 
people do." I will name two of my atrocities : I took one 
of those butter-dishes which have for a top a dome with 
holes in it, which is turned inward, out of reach of accident, 
when not in use. Turning the dome inwards, I filled the 
dish with water, and put a sponge in the dome: the holes 
let it fill with water, and I had a penwiper, always moist, 
and worth its price five times over. "Why! what do you 
mean ? It was made to hold butter. You ' are always at 
some queer thing or other!" I bought a leaden comb, in- 
tended to dye the hair, it being supposed that the applica- 
tion of lead will have this effect. I did not try: but I 
divided the comb into two, separated the part of closed 
prongs from the other ; and thus I had two ruling machines. 
The lead marks paper, and by drawing the end of one of the 
machines along a ruler, I could rule twenty lines at a time, 
quite fit to write on. I thought I should have killed a friend 
to whom I explained it: he could not for the life of him 
understand how leaden lines on paper would dye the hair. 

But Dr. Milner went beyond me. He wanted a seat 
suited to his shape, and he defied opinion to a fearful point. 

1 Isaac Milner (1750-1820) was professor of natural philosophy 
at Cambridge (1783) and later became, as De Morgan states, presi- 
dent of Queens' College (1788). In 1791 he became dean of Carlisle, 
and in 1798 Lucasian professor of mathematics. His chief interest 
was in chemistry and physics, but he contributed nothing of impor- 
tance to these sciences or to mathematics. 



252 A BUDGET OF PARADOXES. 

He spread a thick block of putty over a wooden chair and 
sat in it until it had taken a ceroplast copy of the proper 
seat. This he gave to a carpenter to be imitated in wood. 
One of the few now living who knew him my friend, 
General Perronet Thompson 2 answers for the wood, which 
was shown him by Milner himself ; but he does not vouch 
for the material being putty, which was in the story told 
me at Cambridge ; William Frend 8 also remembered it. Per- 
haps the Doctor took off his great seal in green wax, like 
the Crown; but some soft material he certainly adopted; 
and very comfortable he found the wooden copy. 

The same gentleman vouches for Milner's lamp: but 
this had visible science in it; the vulgar 
see no science in the construction of the 
chair. A hollow semi-cylinder, but not 
with a circular curve, revolved on pivots. 
The curve was calculated on the law 
that, whatever quantity of oil might be 
in the lamp, the position of equilibrium 
just brought the oil up to the edge of 
the cylinder, at which a bit of wick was 
placed. As the wick exhausted the oil, 
the cylinder slowly revolved about the 
pivots so as to keep the oil always touching the wick. 

Great discoveries are always laughed at; but it is very 
often not the laugh of incredulity; it is a mode of dis- 
torting the sense of inferiority into a sense of superiority, 
or a mimicry of superiority interposed between the laugher 
and his feeling of inferiority. Two persons in conversation 

"Thomas Perronet Thompson (1783-1869), fellow of Queens' 
College, Cambridge, saw service in Spain and India, but after 1822 
lived in England. He became major general in 1854, and general in 
1868. Besides some works on economics and politics he wrote a 
Geometry without Axioms (1830) that De Morgan includes later on 
in his Budget. In it Thompson endeavored to prove the parallel 
postulate. 

8 De Morgan's father-in-law. See note i, page 196. 




DR. MILNER'S PARADOXES. 253 

agreed that it was often a nuisance not to be able to lay 
hands on a bit of paper to mark the place in a book, every 
bit of paper on the table was sure to contain something not 
to be spared. I very quietly said that I always had a stock 
of bookmarkers ready cut, with a proper place for them: 
my readers owe many of my anecdotes to this absurd prac- 
tice. My two colloquials burst into a fit of laughter ; about 
what ? Incredulity was out of the question ; and there could 
be nothing foolish in my taking measures to avoid what they 
knew was an inconvenience. I was in this matter obviously 
their superior, and so they laughed at me. Much more 
candid was the Royal Duke of the last century, who was 
noted for slow ideas. "The rain comes into my mouth," 
said he, while riding. "Had not your Royal Highness better 
shut your mouth?" said the equerry. The Prince did so, 
and ought, by rule, to have laughed heartily at his adviser ; 
instead of this, he said quietly, "It doesn't come in now." 

HERBART'S MATHEMATICAL PSYCHOLOGY. 

De Attentionis mensura causisque primariis. By J. F. Herbart. 1 
Koenigsberg, 1822, 4to. 

1 Johann Friedrich Herbart (1776-1841), successor of Kant as 
professor of philosophy at Konigsberg (1809-1833), where he estab- 
lished a school of pedagogy. From 1833 until ms death he was pro- 
fessor of philosophy at Gottingen. The title of the pamphlet is : De 
Attentionis mensura causisque primariis. Psychologiae principia sta- 
tica et mechanica exemplo illustraturus . . . .Regiomonti,. . . .1822. The 
formulas in question are given on pages 15 and 17, and De Morgan 
has omitted the preliminary steps, which are, for the first one : 



unde 



Pro /=0 etiam ^ = 0; hinc /3/ = log. -. 



Tt-<* ' 

These are, however, quite elementary as compared with other 
portions of the theory. 



254 A BUDGET OF PARADOXES. 

This celebrated philosopher maintained that mathematics 
ought to be applied to psychology, in a separate tract, pub- 
lished also in 1822: the one above seems, therefore, to be 
his challenge on the subject. It is on attention, and I think 
it will hardly support Herbart's thesis. As a specimen of 
his formula, let t be the time elapsed since the consideration 
began, /? the whole perceptive intensity of the individual, 
< the whole of his mental force, and z the force given to a 
notion by attention during the time t. Then, 



Now for a test. There is a jactura, v, the meaning of which 
I do not comprehend. If there be anything in it, my mathe- 
matical readers ought to interpret it from the formula 



and to this task I leave them, wishing them better luck than 
mine. The time may come when other manifestations of 
mind, besides belief, shall be submitted to calculation: at 
that time, should it arrive, a final decision may be passed 
upon Herbart. 

ON THE WHIZGIG. 

The theory of the Whizgig considered ; in as much as it mechan- 
ically exemplifies the three working properties of nature; 
which are now set forth under the guise of this toy, for 
children of all ages. London, 1822, I2mo (pp. 24, B. McMil- 
lan, Bow Street, Covent Garden). 

The toy called the whizgig will be remembered by many. 
The writer is a follower of Jacob Behmen, 1 William Law, 2 

1 See note 3, page 168. 

'William Law (1686-1761) was a clergyman, a fellow of Emanuel 
College, Cambridge, and in later life a convert to Behmen's philos- 
ophy. He was so free in his charities that the village in which he 
lived became so infested by beggars that he was urged by the citi- 
zens to leave. He wrote A serious call to a devout and holy life 
(1728). 



ON THE WHIZGIG. 255 

Richard Clarke, 3 and Eugenius Philalethes. 4 Jacob Behmen 
first announced the three working properties of nature, 
which Newton stole, as described in the Gentleman's Maga- 
zine, July, 1782, p. 329. These laws are illustrated in the 
whizgig. There is the harsh astringent, attractive com- 
pression ; the bitter compunction, repulsive expansion ; and 
the stinging anguish, duplex motion. The author hints that 
he has written other works, to which he gives no clue. I 
have heard that Behmen was pillaged by Newton, and Swe- 
denborg 5 by Laplace, 6 and Pythagoras by Copernicus, 7 and 
Epicurus by Dalton, 8 &c. I do not think this mention will 
revive Behmen ; but it may the whizgig, a very pretty toy, 
and philosophical withal, for few of those who used it could 
explain it. 

8 He was a curate at Cheshunt, and wrote the Spiritual voice 
to the Christian Church and to the Jews (London, 1760), A second 
warning to the world by the Spirit of Prophecy (London, 1760), and 
Signs of the Times; or a Voice to Babylon (London, 1773)* 

4 His real name was Thomas Vaughan (1622-1666). He was a 
fellow of Jesus College, Oxford, taking orders, but was deprived 
of his living on account of drunkenness. He became a mystic phi- 
losopher and gave attention to alchemy. His works had a large 
circulation, particularly on the continent. He wrote Magia Adamica 
(London, 1650), Euphrates; or the Waters of the East (London, 
1655), and The Chy mist's key to shut, and to open; or the True Doc- 
trine of Corruption and Generation (London, 1657). 

5 Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. 
It is not commonly known to mathematicians that he was one of 
their guild, but he wrote on both mathematics and chemistry. Among 
his works are the Regelkonst eller algebra (Upsala, 1718) and the 
Methodus nova inveniendi longitudines locorum, terra marique, ope 
lunae (Amsterdam, 1721, 1727, and 1766). After 1747 he devoted 
his attention to mystic philosophy. 

6 Pierre Simon Laplace (1749-1827), whose Exposition du sys- 
teme du monde (1796) and Traite de mecanique celeste (1799) are 
well known. 

7 See note 3, page 76. 

8 John Dalton (1766-1844), who taught mathematics and physics 
at New College, Manchester (1793-1799) and was the first to state 
the law of the expansion of gases known by his name and that of 
Gay-Lussac. His New system of Chemical Philosophy (Vol. I, pt. i, 
1808; pt. ii, 1810; vol. II, 1827) sets forth his atomic theory. 



256 A BUDGET OF PARADOXES. 

SOME MYTHOLOGICAL PARADOXES. 

A Grammar of infinite forms; or the mathematical elements of 
ancient philosophy and mythology. By Wm. Howison. 1 Edin- 
burgh, 1823, 8vo. 

A curius combination of geometry and mythology. Per- 
seus, for instance, is treated under the head, "the evolution 
of diminishing hyperbolic branches." 

The Mythological Astronomy of the Ancients; part the second: 

or the key of Urania, the words of which will unlock all the 

mysteries of antiquity. Norwich, 1823, I2mo. 
A Companion to the Mythological Astronomy, &c., containing 

remarks on recent publications Norwich, 1824, I2mo. 

A new Theory of the Earth and of planetary motion ; in which it 

is demonstrated that the Sun is vicegerent of his own system. 

Norwich, 1825, I2mo. 
The analyzation of the writings of the Jews, so far as they are 

found to have any connection with the sublime science of 

astronomy. [This is pp. 97-180 of some other work, being all 

I have seen.] 

These works are all by Sampson Arnold Mackey, 2 for 
whom see Notes and Queries, 1st S. viii. 468, 565, ix. 89, 
179. Had it not been for actual quotations given by one 
correspondent only (1st S. viii. 565), that journal would 
have handed him down as a man of some real learning. An 
extraordinary man he certainly was: it is not one illiterate 
shoemaker in a thousand who could work upon such a sin- 
gular mass of Sanskrit and Greek words, without showing 

1 Howison was a poet and philosopher. He lived in Edinburgh 
and was a friend of Sir Walter Scott. This work appeared in 1822. 

3 He was a shoemaker, born about 1765 at Haddiscoe, and his 
"astro-historical" lectures at Norwich attracted a good deal of atten- 
tion at one time. He traced all geologic changes to differences in 
the inclination of the earth's axis to the plane of its orbit. Of the 
works mentioned by De Morgan the first appeared at Norwich in 
1822-1823, and there was a second edition in 1824. The second 
appeared in 1824-1825. The fourth was Urania's Key to the Reve- 
lation; or the analyzation of the writings of the Jews , and was 

first published at Norwich in 1823, there being a second edition at 
London in 1833. His books were evidently not a financial success, 
for Mackey died in an almshouse at Norwich. 



SOME MYTHOLOGICAL PARADOXES. 257 

evidence of being able to read a line in any language but 
his own, or to spell that correctly. He was an uneducated 
Godfrey Higgins. 3 A few extracts will put this in a strong 
light: one for history of science, one for astronomy, and 
one for philology: 

"Sir Isaac Newton was of opinion that 'the atmosphere 
of the earth was the sensory of God ; by which he was en- 
abled to see quite round the earth:' which proves that Sir 
Isaac had no idea that God could see through the earth. 

"Sir Richard [Phillips] has given the most rational ex- 
planation of the cause of the earth's elliptical orbit that I 
have ever seen in print. It is because the earth presents its 
watery hemisphere to the sun at one time and that of solid 
land the other ; but why has he made his Oxonian astonished 
at the coincidence? It is what I taught in my attic twelve 
years before. 

"Again, admitting that the Eloim were powerful and in- 
telligent beings that managed these things, we would accuse 
them of being the authors of all the sufferings of Chrisna. 
And as they and the constellation of Leo were below the 
horizon, and consequently cut off from the end of the 
zodiac, there were but eleven constellations of the zodiac 
to be seen ; the three at the end were wanted, but those three 
would be accused of bringing Chrisna into the troubles which 
at last ended in his death. All this would be expressed in 
the Eastern language by saying that Chrisna was persecuted 
by those Judoth Ishcarioth ! ! ! ! ! [the five notes of exclama- 
tion are the author's]. But the astronomy of those distant 
ages, when the sun was at the south pole in winter, would 
leave five of those Decans cut off from our view, in the 
latitude of twenty-eight degrees; hence Chrisna died of 

8 Godfrey Higgins (1773-1833), the archeologist, was interested 
in the history of religious beliefs and in practical sociology. He 
wrote Horae Sabbaticae (1826), The Celtic Druids (1827 and 1829), 
and Anacalypsis^ an attempt to draw aside the veil of the Saitic 
Isis; or an Inquiry into the Origin of Languages, Nations, and Re- 
ligions (posthumously published, 1836), and other works. See also 
page 274, infra. 



258 A BUDGET OF PARADOXES. 

wounds from five Decans, but the whole five may be in- 
cluded in Judoth Ishcarioth ! for the phrase means 'the men 
that are wanted at the extreme parts/ Ishcarioth is a com- 
pound of ish, a man, and carat wanted or taken away, and 
oth the plural termination, more ancient than im . . . . " 

I might show at length how. Michael is the sun, and the 
D'-ev-'l in French Di-ob-al, also 'L-evi-ath-an the evi 
being the radical part both of devil and Imathan is the 
Nile, which the sun dried up for Moses to pass: a battle 
celebrated by Jude. Also how Moses, the same name as 
Muses, is from mesha, drawn out of the water, "and hence 
we called our land which is saved from the water by the 
name of marsh!' But it will be of more use to collect the 
character of S. A. M. from such correspondents of Notes 
and Queries as have written after superficial examination. 
Great astronomical and philological attainments, much abil- 
ity and learning; had evidently read and studied deeply; 
remarkable for the originality of his views upon the very 
abstruse subject of mythological astronomy, in which he 
exhibited great sagacity. Certainly his views were original ; 
but their sagacity, if it be allowable to copy his own mode 
of etymologizing, is of an ori-gin-ale cast, resembling that of 
a person who puts to his mouth liquors both distilled and 
fermented. 

A KANTESIAN JEWELER. 

Principles of the Kantesian, or transcendental philosophy. By 
Thomas Wirgman. 1 London, 1824, 8vo. 

Mr. Wirgman's mind was somewhat attuned to psychol- 
ogy; but he was cracky and vagarious. He had been a 
fashionable jeweler in St. James's Street, no doubt the son 
or grandson of Wirgman at "the well-known toy-shop in 

J The work also appeared in French. Wirgman wrote, or at 
least began, two other works: Divarication of the New Testament 
into Doctrine and History; part I, The Four Gospels (London, 1830), 
and Mental Philosophy; part I, Grammar of the five senses; being 
the first step to infant education (London, 1838). 



A KANTESIAN JEWELER. 259 

St. James's Street/* where Sam Johnson smartened himself 
with silver buckles. (Boswell, at. 69). He would not have 
the ridiculous large ones in fashion; and he would give no 
more than a guinea a pair; such, says Boswell, in Italics, 
were the principles of the business: and I think this may 
be the first place in which the philosophical word was brought 
down from heaven to mix with men. However this may 
be, my Wirgman sold snuff-boxes, among other things, and 
fifty years ago a fashionable snuff-boxer would be under 
inducement, if not positively obliged, to have a stock with 
very objectionable pictures. So it happened that Wirgman 
by reason of a trifle too much candor came under the 
notice of the Suppression Society, and ran considerable risk. 
Mr. Brougham was his counsel ; and managed to get him 
acquitted. Years and years after this, when Mr. Brougham 
was deep in the formation of the London University (now 
University College), Mr. Wirgman called on him. "What 
now?" said Mr. B. with his most sarcastic look a very 
perfect thing of its kind "you're in a scrape again, I sup- 
pose!" "No! indeed!" said W., "my present object is to 
ask your interest for the chair of Moral Philosophy in the 
new University!" He had taken up Kant! 

Mr. Wirgman, an itinerant paradoxer, called on me in 
1831 : he came to convert me. "I assure you," said he, 
"I am nothing but an old brute of a jeweler;" and his eye 
and manner were of the extreme of jocosity, as good in their 
way, as the satire of his former counsel. I mention him as 
one of that class who go away quite satisfied that they have 
wrought conviction. "Now," said he, "I'll make it clear to 
you! Suppose a number of gold-fishes in a glass bowl, 
you understand? Well! I come with my cigar and go 
puff, puff, puff, over the bowl, until there is a little cloud 
of smoke: now, tell me, what will the gold-fishes say to 
that?" "I should imagine," said I, "That they would not 
know what to make of it." "By Jove! you're a Kantian;" 
said he, and with this and the like, he left me, vowing that 



260 A BUDGET OF PARADOXES. 

it was delightful to talk to so intelligent a person. The 
greatest compliment Wirgman ever received was from James 
Mill, who used to say he did not understand Kant. That 
such a man as Mill should think this worth saying is a 
feather in the cap of the jocose jeweler. 

Some of my readers will stare at my supposing that 
Boswell may have been the first down-bringer of the word 
principles into common life ; the best answer will be a prior 
instance of the word as true vernacular ; it has never hap- 
pened to me to notice one. Many words have very com- 
mon uses which are not old. Take the following from 
Nichols (Anecd. ix. 263) : "Lord Thurlow presents his best 
respects to Mr. and Mrs. Thicknesse, and assures them that 
he knows of no cause to complain of any part of Mr. Thick- 
nesse's carriage; least of all the circumstance of sending 
the head to Ormond Street." Surely Mr. T. had lent Lord 
T. a satisfactory carriage with a movable head, and the 
above is a polite answer to inquiries. Not a bit of it! car- 
riage is here conduct, and the head is a bust. The vehicles 
of the rich, at the time, were coaches, chariots, chaises, etc., 
never carriages, which were rather carts. Gibbon has the 
word for baggage-wagons. In Jane Austen's novels the 
word carriage is established. 

WALSH'S DELUSIONS. 

John Walsh, 1 of Cork (1786-1847). This discoverer 
has had the honor of a biography from Professor Boole, 
who, at my request, collected information about him on the 
scene of his labors. It is in the Philosophical Magazine for 
November, 1851, and will, I hope, be transferred to some 
biographical collection where it may find a larger class of 
readers. It is the best biography of a single hero of the 
kind that I know. Mr. Walsh introduced himself to me, 

a He was born at Shandrum, County Limerick, and supported 
himself by teaching writing and arithmetic. He died in an almshouse 
at Cork. 



WALSH'S DELUSIONS. 261 

as he did to many others, in the anterowlandian days of the 
Post-office ; his unpaid letters were double, treble, &c. They 
contained his pamphlets, and cost their weight in silver: all 
have the name of the author, and all are in octavo or in 
quarto letter- form: most are in four pages, and all dated 
from Cork. I have the following by me: 

The Geometric .Base, 1825. The theory of plane angles. 1827. 
Three Letters to Dr. Francis Sadleir. 1838. The invention 
of polar geometry. By Irelandus. 1839. The theory of par- 
tial functions. Letter to Lord Brougham. 1839. On the in- 
vention of polar geometry. 1839. Letter to the Editor of the 
Edinburgh Review. 1840. Irish Manufacture. A new method 
of tangents. 1841. The normal diameter in curves. 1843. 
Letter to Sir R. Peel. 1845. [Hints that Government should 
compel the introduction of Walsh's Geometry into Universi- 
ties.] Solution of Equations of the higher orders. 1845. 

Besides these, there is a Metalogia, and I know not how 
many others. 

Mr. Boole, 2 who has taken the moral and social fea- 
tures of Walsh's delusions from the commiserating point 
of view, which makes ridicule out of place, has been obliged 
to treat Walsh as Scott's Alan Fairford treated his client 
Peter Peebles; namely, keep the scarecrow out of court 
while the case was argued. My plan requires me to bring 
him in : and when he comes in at the door, pity and sym- 
pathy fly out at the window. Let the reader remember 
that he was not an ignoramus in mathematics: he might 
have won his spurs if he could have first served as an es- 
quire. Though so illiterate that even in Ireland he never 
picked up anything more Latin than Irelandus, he was a 
very pretty mathematician spoiled in the making by intense 
self-opinion. 

This is part of a private letter to me at the back of a 
page of print: I had never addressed a word to him: 

8 George Boole (1815-1864), professor of mathematics at Queens' 
College, Cork. His Laws of Thought (1854) was the first work on 
the algebra of logic. 



262 A BUDGET OF PARADOXES. 

"There are no limits in mathematics, and those that 
assert there are, are infinite ruffians, ignorant, lying black- 
guards. There is no differential calculus, no Taylor's the- 
orem, no calculus of variations, &c. in mathematics. There 
is no quackery whatever in mathematics ; no % equal to 
anything. What sheer ignorant blackguardism that! 

"In mechanics the parallelogram of forces is quackery, 
and is dangerous ; for nothing is at rest, or in uniform, or 
in rectilinear motion, in the universe. Variable motion is 
an essential property of matter. Laplace's demonstration 
of the parallelogram of forces is a begging of the question ; 
and the attempts of them all to show that the difference 
of twenty minutes between the sidereal and actual revolu- 
tion of the earth round the sun arises from the tugging of 
the Sun and Moon at the pot-belly of the earth, without 
being sure even that the earth has a pot-belly at all, is 
perfect quackery. The said difference arising from and 
demonstrating the revolution of the Sun itself round some 
distant center." 

In the letter to Lord Brougham we read as follows: 

"I ask the Royal Society of London, I ask the Saxon 
crew of that crazy hulk, where is the dogma of their phil- 
osophic god now? When the Royal Society of London, 

and the Academy of Sciences of Paris, shall have read this 
memorandum, how will they appear? Like two cur dogs 

in the paws of the noblest beast of the forest Just as 

this note was going to press, a volume lately published by 
you was put into my hands, wherein you attempt to defend 
the fluxions and Principia of Newton. Man ! what are you 
about? You come forward now with your special pleading, 
and fraught with national prejudice, to defend, like the 
philosopher Grassi, 3 the persecutor of Galileo, principles 

'Oratio Grassi (1582-1654), the Jesuit who became famous for 
his controversy with Galileo over the theory of comets. Galileo 
ridiculed him in // Saggiatore, although according to the modern 
view Grassi was the more nearly right It is said that the latter's 
resentment led to the persecution of Galileo. 



WALSH'S DELUSIONS. 263 

and reasoning which, unless you are actually insane, or an 
ignorant quack in mathematics, you know are mathemat- 
ically false. What a moral lesson this for the students of 
the University of London from its head ! Man ! demonstrate 
corollary 3, in this note, by the lying dogma of Newton, or 
turn your thoughts to something you understand. 

"WALSH IRELANDUS." 

Mr. Walsh honor to his memory once had the con- 
sideration to save me postage by addressing a pamphlet 
under cover to a Member of Parliament, with an explana- 
tory letter. In that letter he gives a candid opinion of 
himself : 

(1838.) "Mr. Walsh takes leave to send the enclosed 
corrected copy to Mr. Hutton as one of the Council of the 
University of London, and to save postage for the Pro- 
fessor of Mathematics there. He will find in it geometry 
more deep and subtle, and at the same time more simple and 
elegant, than it was ever contemplated human genius could 
invent." 

He then proceeds to set forth that a certain "tomfoolery 
lemma," with its "tomfoolery" superstructure, "never had 
existence outside the shallow brains of its inventor," Euclid. 
He then proceeds thus: 

"The same spirit that animated those philosopher^ who 
sent Galileo to the Inquisition animates all the philosophers 
of the present day without exception. If anything can free 
them from the yoke of error, it is the [Walsh] problem of 
double tangence. But free them it will, how deeply soever 
they may be sunk into mental slavery and God knows that 
is deeply enough ; and they bear it with an admirable grace ; 
for none bear slavery with a better grace than tyrants. The 
lads must adopt my theory .... It will be a sad reverse for 
all our great professors to be compelled to become school- 
boys in their gray years. But the sore scratch is to be com- 
pelled, as they had before been compelled one thousand 
years ago, to have recourse to Ireland for instruction." 



264 A BUDGET OF PARADOXES. 

The following "Impromptu" is no doubt by Walsh him- 
self : he was more of a poet than of an astronomer : 

"Through ages unfriended, 

With sophistry blended, 
Deep science in Chaos had slept; 

Its limits were fettered, 

Its voters unlettered, 
Its students in movements but crept. 

Till, despite of great foes, 

Great WALSH first arose, 
And with logical might did unravel 

Those mazes of knowledge, 

Ne'er known in a college, 
Though sought for with unceasing travail. 

With cheers we now hail him, 

May success never fail him, 
In Polar Geometrical mining; 

Till his foes be as tamed 

As his works are far-famed 
For true philosophic refining." 

Walsh's system is, that all mathematics and physics are 
wrong: there is hardly one proposition in Euclid which is 
demonstrated. His example ought to warn all who rely on 
their own evidence to their own success. He was not, 
properly speaking, insane; he only spoke his mind more 
freely -than many others of his class. The poor fellow died 
in the Cork union, during the famine. He had lived a happy 
life, contemplating his own perfections, like Brahma on the 
lotus-leaf. 4 

*De Morgan might have found much else for his satire in the 
letters of Walsh. He sought, in his Theory of Partial Functions, to 
substitute "partial equations" for the differential calculus. In his 
diary there is an entry: "Discovered the general solution of numer- 
ical equations of the fifth degree at 114 Evergreen Street, at the 
Cross of Evergreen, Cork, at nine o'clock in the forenoon of July 7th, 
1844 ; exactly twenty-two years after the invention of the Geometry 
of Partial Equations, and the expulsion of the differential calculus 
from Mathematical Science." 



GROWTH OF FREEDOM OF OPINION. 265 



GROWTH OF FREEDOM OF OPINION. 

The year 1825 brings me to about the middle of my 
Athenaeum list: that is, so far as mere number of names 
mentioned is concerned. Freedom of opinion, beyond a doubt, 
is gaining ground, for good or for evil, according to what 
the speaker happens to think: admission of authority is no 
longer made in the old way. If we take soul-cure and body- 
cure, divinity and medicine, it is manifest that a change 
has come over us. Time was when it was enough that dose 
or dogma should be certified by "II a ete ordonne, Mon- 
sieur, il a ete ordonne," 1 as the apothecary said when he 
wanted to operate upon poor de Porceaugnac. Very much 
changed: but whether for good or for evil does not now 
matter; the question is, whether contempt of demonstration 
such as our paradoxers show has augmented with the re- 
jection of dogmatic authority. It ought to be just the 
other way : for the worship of reason is the system on which, 
if we trust them, the deniers of guidance ground their plan 
of life. The following attempt at an experiment on this 
point is the best which I can make ; and, so far as I know, 
the first that ever was made. 

Say that my list of paradoxers divides in 1825: this of 
itself proves nothing, because so many of the earlier books 
are lost, or not likely to be come at. It would be a fearful 
rate of increase which would make the number of paradoxes 
since 1825 equal to the whole number before that date. Let 
us turn now to another collection of mine, arithmetical books, 
of which I have published a list. The two collections are 
similarly circumstanced as to new and old books ; the para- 
doxes had no care given to the collection of either; the 
arithmetical books equal care to both. The list of arith- 
metical books, published in 1847, divides at 1735 ; the para- 
doxes, up to 1863, divide at 1825. If we take the process 
which is most against the distinction, and allow every year 

1 "It has been ordered, sir, it has been ordered." 



266 A BUDGET OF PARADOXES. 

from 1847 to 1863 to add a year to 1735, we should say that 
the arithmetical writers divide at 1751. This rough process 
may serve, with sufficient certainty, to show that the propor- 
tion of paradoxes to books of sober demonstration is on the 
increase; and probably, quite as much as the proportion of 
heterodoxes to books of orthodox adherence. So that di- 
vinity and medicine may say to geometry, Don't you sneer : 
if rationalism, homoeopathy, and their congeners are on the 
rise among us, your enemies are increasing quite as fast. But 
geometry replies Dear friends, content yourselves with the 
rational inference that the rise of heterodoxy within your 
pales is not conclusive against you, taken alone ; for it rises 
at the same time within mine. Store within your garners 
the precious argument that you are not proved wrong 
by increase of dissent; because there is increase of dissent 
against exact science. But do not therefore even yourselves 
to me: remember that you, Dame Divinity, have inflicted 
every kind of penalty, from the stake to the stocks, in aid 
of your reasoning; remember that you, Mother Medicine, 
have not many years ago applied to Parliament for increase 
of forcible hindrance of antipharmacopceal drenches, pills, 
and powders. Who ever heard of my asking the legislature 
to fine blundering circle-squarers ? Remember that the D 
in dogma is the D in decay ; but the D in demonstration is 
the D in durability. 

THE STATUS OF MEDICINE. 

I have known a medical man a young one who was 
seriously of the opinion that the country ought to be divided 
into medical parishes, with a practitioner appointed to each, 
and a penalty for calling in any but the incumbent curer. 
How should people know how to choose ? The hair-dressers 
once petitioned Parliament for an act to compel people to 
wear wigs. My own opinion is of the opposite extreme, as 
in the following letter (Examiner, April 5, 1856) ; which, 
to my surprise, I saw reprinted in a medical journal, as a 



THE STATUS OF MEDICINE. 267 

plan not absolutely to be rejected. I am perfectly satis- 
fied that it would greatly promote true medical orthodoxy, 
the predominance of well educated thinkers, and the de- 
velopment of their desirable differences. 

"SiR. The Medical Bill and the medical question gen- 
erally is one on which experience would teach, if people 
would be taught. 

"The great soul question took three hundred years to 
settle: the little body question might be settled in thirty 
years, if the decisions in the former question were studied. 

"Time was when the State believed, as honestly as ever 
it believed anything, that it might, could, and should find 
out the true doctrine for the poor ignorant community; to 
which, like a worthy honest state, it added would. Accord- 
ingly, by the assistance of the Church, which undertook the 
physic, the surgery, and the pharmacy of sound doctrine all 
by itself, it sent forth its legally qualified teachers into every 
parish, and woe to the man who called in any other. They 
burnt that man, they whipped him, they imprisoned him, 
they did everything but what was Christian to him, all for 
his soul's health and the amendment of his excesses. 

"But men would not submit. To the argument that the 
State was a father to the ignorant, they replied that it was 
at best the ignorant father of an ignorant son, and that a 
blind man could find his way into a ditch without another 
blind man to help him, And when the State said But 
here we have the Church, which knows all about it, the 
ignorant community declared that it had a right to judge 
that question, and that it would judge it. It also said that 
the Church was never one thing long, and that it progressed, 
on the whole, rather more slowly than the ignorant com- 
munity. 

"The end of it was, in this country, that every one who 
chose taught all who chose to let him teach, on condition 
only of an open and true registration. The State was 



268 A BUDGET OF PARADOXES. 

allowed to patronize one particular Church, so that no one 
need trouble himself to choose a pastor from the mere ne- 
cessity of choosing. But every church is allowed its col- 
leges, its studies, its diplomas; and every man is allowed 
his choice. There is no proof that our souls are worse off 
than in the sixteenth century; and, judging by fruits, there 
is much reason to hope they are better off. 

"Now the little body question is a perfect parallel to the 
great soul question in all its circumstances. The only things 
in which the parallel fails are the following : Every one who 
believes in a future state sees that the soul question is in- 
comparably more important than the body question, and 
every one can try the body question by experiment to a 
larger extent than the soul question. The proverb, which 
always has a spark of truth at the bottom, says that every 
man of forty is either a fool or a physician; but did even 
the proverb maker ever dare to say that every man is at any 
age either a fool or a fit teacher of religion? 

"Common sense points out the following settlement of 
the medical question: and to this it will come sooner or 
later. 

"Let every man who chooses subject to one common 
law of manslaughter for all the crass cases doctor the 
bodies of all who choose to trust him, and recover payment 
according to agreement in the courts of law. Provided 
always that every person practising should be registered 
at a moderate fee in a register to be republished every six 
months. 

"Let the register give the name, address, and asserted 
qualification of each candidate as licentiate, or doctor, or 
what not, of this or that college, hall, university, &c., home 
or foreign. Let it be competent to any man to describe 
himself as qualified by study in public schools without a 
diploma, or by private study, or even by intuition or divine 
inspiration, if he please. But whatever he holds his quali- 
fication to be, that let him declare. Let all qualification 



THE STATUS OF MEDICINE. 269 

which of its own nature admits of proof be proved, as by 
the diploma or certificate, &c., leaving things which cannot 
be proved, as asserted private study, intuition, inspiration, 
&c., to work their own way. 

"Let it be highly penal to assert to the patient any quali- 
fication which is not in the register, and let the register be 
sold very cheap. Let the registrar give each registered prac- 
titioner a copy of the register in his own case ; let any patient 
have the power to demand a sight of this copy ; and let no 
money for attendance be recoverable in any case in which 
there has been false representation. 

"Let any party in any suit have a right to produce what 
medical testimony he pleases. Let the medical witness pro- 
duce his register, and let his evidence be for the jury, as is 
that of an engineer or a practitioner of any art which is not 
attested by diplomas. 

"Let any man who practises without venturing to put 
his name on the register be liable to fine and imprisonment. 

"The consequence would be that, as now, anybody who 
pleases might practise ; for the medical world is well aware 
that there is no power of preventing what they call quacks 
from practising. But very different from what is now, 
every man who practises would be obliged to tell the whole 
world what his claim is, and would run a great risk if he 
dared to tell his patient in private anything different from 
what he had told the whole world. 

"The consequence would be that a real education in 
anatomy, physiology, chemistry, surgery, and what is known 
of the thing called medicine, would acquire more impor- 
tance than it now has. 

"It is curious to see how completely the medical man 
of the nineteenth century squares with the priest of the 
sixteenth century. The clergy of all sects are now better 
divines and better men than they ever were. They have lost 
Bacon's reproach that they took a smaller measure of things 
than any other educated men ; and the physicians are now 



270 A BUDGET OF PARADOXES. 

in this particular the rearguard of the learned world ; though 
it may be true that the rear in our day is further on in the 
march than the van of Bacon's day. Nor will they ever 
recover the lost position until medicine is as free as religion. 
"To this it must come. To this the public, which will 
decide for itself, has determined it shall come. To this the 
public has, in fact, brought it, but on a plan which it is not 
desirable to make permanent. We will be as free to take 
care of our bodies as of our souls and of our goods. This 
is the profession of all who sign as I do, and the practice 
of most of those who would not like the name 

"HETEROPATH." 

The motion of the Sun in the Ecliptic, proved to be uniform in 
a circular orbit. . . .with preliminary observations on the fallacy 
of the Solar System. By Bartholomew Prescott, 1 1825, 8vo. 

The author had published, in 1803, a Defence of the 
Divine System, which I never saw; also, On the inverted 
scheme of Copernicus. The above work is clever in its 
satire. 

THE CHRISTIAN EVIDENCE SOCIETY. 

Manifesto of the Christian Evidence Society, established Nov. 
12, 1824. Twenty-four plain questions to honest men. 

These are two broadsides of August and November, 
1826, signed by Robert Taylor, 1 A. B., Orator of the Chris- 
tian Evidence Society. This gentleman was a clergyman, 

1 Bartholomew Prescot was a Liverpool accountant. De Morgan 
gives this correct spelling 9n page 278. He died after 1849. His 
Inverted Scheme of Copernicus appeared in Liverpool in 1822. 

1 Robert Taylor (1784-1844) had many more ups and downs than 
De Morgan mentions. He was a priest of the Church of England, 
but resigned his parish in 1818 after preaching against Christianity. 
He soon recanted and took another parish, but was dismissed by the 
Bishop almost immediately on the ground of heresy. As stated in 
the text, he was convicted of blasphemy in 1827 and was sentenced 
to a year's imprisonment, and again for two years on the same 
charge in 1831. He then married a woman who was rich in money 
and in years, and was thereupon sued for breach of promise by 
another woman. To escape paying the judgment that was rendered 
against him he fled to Tours where he took up surgery. 



THE CHRISTIAN EVIDENCE SOCIETY. 271 

and was convicted of blasphemy in 1827, for which he suf- 
fered imprisonment, and got the name of the Devil's Chap- 
lain. The following are quotations : 

"For the book of Revelation, there was no original Greek 
at all, but Erasmus wrote it himself in Switzerland, in the 
year 1516. Bishop Marsh, 2 vol. i. p. 320." "Is not God the 
author of your reason ? Can he then be the author of any- 
thing which is contrary to your reason? If reason be a 
sufficient guide, why should God give you any other? if it 
be not a sufficient guide, why has he given you that?" 

1 remember a votary of the Society being asked to substi- 
tute for reason "the right leg," and for guide "support," 
and to answer the two last questions: he said there must 
be a quibble, but he did not see what. It is pleasant to 
reflect that the argumentum a carcere 3 is obsolete. One 
great defect of it was that it did not go far enough: there 
should have been laws against subscriptions for blasphemers, 
against dealing at their shops, and against rich widows 
marrying thefn. 

Had I taken in theology, I must have entered books 
against Christianity. I mention the above, and Paine's 
Age of Reason, simply because they are the only English 
modern works that ever came in my way without my ask- 
ing for them. The three parts of the Age of Reason 
were published in Paris 1793, Paris 1795, and New York 
1807. CarlileV edition is of London, 1818, 8vo. It must 
be republished when the time comes, to show what stuff 
governments and clergy were afraid of at the beginning 
of this century. I should never have seen the book, if it 

2 Herbert Marsh, Bishop of Peterborough. See note 9 on page 
199. 

3 "Argument from the prison." 

4 Richard Carlile (1790-1843), one of the leading radicals of his 
time. He published Hone's parodies (see note 9, page 124) after 
they had been suppressed, and an edition of Thomas Paine (1818). 
He was repeatedly imprisoned, serving nine years in all. His con- 
tinued conflict with the authorities proved a good advertisement 
for his bookshop. 



272 A BUDGET OF PARADOXES. 

had not been prohibited : a bookseller put it under my nose 
with a fearful look round him; and I could do no less, in 
common curiosity, than buy a work which had been so com- 
plimented by church and state. And when I had read it, 
I said in my mind to church and state, Confound you! 
you have taken me in worse than any reviewer I ever met 
with. I forget what I gave for the book, but I ought to 
have been able to claim compensation somewhere. 

THE CABBALA. 

Cabbala Algebraica. Auctore Gul. Lud. Christmann. 1 Stutt- 
gard, 1827, 4to. 

Eighty closely printed pages of an attempt to solve equa- 
tions of every degree, which has a process called by the 
author cabbala. An anonymous correspondent spells cab- 
bala as follows, xa/?/?aAA, and makes 666 out of its letters. 
This gentleman has sent me since my Budget commenced, 
a little heap of satirical communications, each having a 666 
or two ; for instance, alluding to my remarks on the spelling 
of chemistry, he finds the fated number in xw* l(J ~ With these 
are challenges to explain them, and hints about the end of the 
world. All these letters have different fantastic seals ; one 
of them with the legend "keep your temper," another 
bearing "bank token five pence." The only signature is a 
triangle with a little circle in it, which I interpret to mean 
that the writer confesses himself to be the round man stuck 
in the three-cornered hole, to be explained as in Sydney 
Smith's joke. 

1 Wilhelm Ludwig Christmann (1780-1835) was a protestant 
clergyman and teacher of mathematics. For a while he taught under 
Pestalozzi. Disappointed in his ambition to be professor of mathe- 
matics at Tubingen, he became a confirmed misanthrope and is said 
never to have left his house during the last ten years of his life. He 
wrote several works : Ein Wort tiber Pestalozzi und Pestalozzismus 
(1812); Ars cossae promota (1814); Philosophic, cossica (1815); 
Aetas argentea cossae (1819); Ueber Tradition und Schrift, Logos 
und Kabbala (1829), besides the one mentioned above. The word 
coss in the above titles was a German name for algebra, from the 
Italian cosa (thing), the name for the unknown quantity. It appears 
in English in the early name for algebra, "the cossic art." 



THE CABBALA. 273 

There is a kind of Cabbala Alphabetica which the in- 
vestigators of the numerals in words would do well to take 
up: it is the formation of sentences which contain all the 
letters of the alphabet, and each only once. No one has done 
it with v and / treated as consonants ; but you and I can 
do it. Dr. Whewell 2 and I amused ourselves, some years 
ago, with attempts. He could not make sense, though he 
joined words : he gave me 

Phiz, styx, wrong, buck, flame, quid. 

I gave him the following, which he agreed was "admirable 
sense" : I certainly think the words would never have come 
together except in this way: 

I, quartz pyx, who fling muck beds. 

I long thought that no human being could say this under 
any circumstances. At last I happened to be reading a 
religious writer as he thought himself who threw asper- 
sions on his opponents thick and threefold. Heyday! came 
into my head, this fellow flings muck beds; he must be a 
quartz pyx. And then I remembered that a pyx is a sacred 
vessel, and quartz is a hard stone, as hard as the heart of a 
religious foe-curser. So that the line is the motto of the 
ferocious sectarian, who turns his religious vessels into mud- 
holders, for the benefit of those who will not see what he 
sees. 

1 can find no circumstances for the following, which I 
received from another: 

Fritz! quick! land! hew gypsum box. 
From other quarters I have the following: 
Dumpy quiz! whirl back fogs next. 

This might be said in time of haze to the queer little figure 
in the Dutch weather-toy, which comes out or goes in with 
the change in the atmosphere. Again, 

2 See note 4, page 101. 



274 A BUDGET OF PARADOXES. 

Export my fund! Quiz black whigs. 

This Squire Western might have said, who was always 
afraid of the whigs sending the sinking-fund over to Han- 
over. But the following is the best: it is good advice to 
a young man, very well expressed under the circumstances : 

Get nymph; quiz sad brow; fix luck. 

Which in more sober English would be, Marry ; be cheer- 
ful; watch your business. There is more edification, more 
religion in this than in all the 666-interpretations put to- 
gether. 

Such things would make excellent writing copies, for 
they secure attention to every letter ; v and / might be placed 
at the end. 

ON GODFREY HIGGINS. 

The Celtic Druids. By Godfrey Higgins, 1 Esq. of Skellow 
Grange, near Doncaster. London, 1827, 4to. 

Anacalypsis, or an attempt to draw aside the veil of the Saitic 
Isis : or an inquiry into the origin of languages, nations, and 

religions. By Godfrey Higgins, &c , London, 1836, 2 

vols. 4to. 

The first work had an additional preface and a new index 
in 1829. Possibly, in future time, will be found bound up with 
copies of the second work two sheets which Mr. Higgins 
circulated among his friends in 1831 : the first a "Recapitu- 
lation," the second "Book vi. ch. 1." 

The system of these works is that 

"The Buddhists of Upper India (of whom the Phenician 
Canaanite, Melchizedek, was a priest), who built the Pyra- 
mids, Stonehenge, Carnac, &c. will be shown to have founded 
all the ancient mythologies of the world, which, however 
varied and corrupted in recent times, were originally one, 
and that one founded on principles sublime, beautiful, and 
true." 

1 See note 3, page 257. 



ON GODFREY HIGGINS. 275 

These works contain an immense quantity of learning, 
very honestly put together. I presume the enormous num- 
ber of facts, and the goodness of the index, to be the rea- 
sons why the Anacalypsis found a permanent place in the 
old reading-room of the British Museum, even before the 
change which greatly increased the number of books left 
free to the reader in that room. 

Mr. Higgins, whom I knew well in the last six years 
of his life, and respected as a good, learned, and (in his 
own way) pious man, was thoroughly and completely the 
man of a system. He had that sort of mental connection 
with his theory that made his statements of his authorities 
trustworthy: for, besides perfect integrity, he had no bias 
towards alteration of facts: he saw his system in the way 
the fact was presented to him by his authority, be that 
what it might. 

He was very sure of a fact which he got from any of 
his authorities: nothing could shake him. Imagine a con- 
versation between him and an Indian officer who had paid 
long attention to Hindoo antiquities and their remains: a 
third person was present, ego qui scribo. G. H. "You know 
that in the temples of I-forget-who the Ceres is always 

sculptured precisely as in Greece." Col. , "I really do 

not remember it, and I have seen most of these temples." 
G. H. "It is so, I assure you, especially at I-forget-where." 

Col. , "Well, I am sure! I was encamped for six 

weeks at the gate of that very temple, and, except a little 
shooting, had nothing to do but to examine its details, 
which I did, day after day, and I found nothing of the 
kind." It was of no use at all. 

Godfrey Higgins began life by exposing and conquer- 
ing, at the expense of two years of his studies, some shock- 
ing abuses which existed in the York Lunatic Asylum. 
This was a proceeding which called much attention to the 
treatment of the insane, and produced much good effect. 
He was very resolute and energetic. The magistracy of his 



276 A BUDGET OF PARADOXES. 

time had scruples about using the severity of law to people 
of such station as well-to-do farmers, &c. : they would allow 
a great deal of resistance, and endeavor to mollify the 
rebels into obedience. A young farmer flatly refused to 
pay under an order of affiliation made upon him by Godfrey 
Higgins. He was duly warned; and persisted: he shortly 
found himself in gaol. He went there sure to conquer the 
Justice, and the first thing he did was to demand to see his 
lawyer. He was told, to his horror, that as soon as he had 
been cropped and prison-dressed, he might see as many 
lawyers as he pleased, to be looked at, laughed at, and 
advised that there was but one way out of the scrape. 
Higgins was, in his speculations, a regular counterpart of 
Bailly; but the celebrated Mayor of Paris had not his 
nerve. It is impossible to say, if their characters had been 
changed, whether the unfortunate crisis in which Bailly 
was not equal to the occasion would have led to very differ- 
ent results if Higgins had been in his place: but assuredly 
constitutional liberty would have had one chance more. 
There are two works of his by which he was known, apart 
from his paradoxes. First, An apology for the life and 
character of the celebrated prophet of Arabia, called Mo- 
hamed, or the Illustrious. London, 8vo. 1829. The reader 
will look at this writing of our English Buddhist with sus- 
picious eye, but he will not be able to avoid confessing that 
the Arabian prophet has some reparation to demand at the 
hands of Christians. Next, Hora Sabaticcs; or an attempt 
to correct certain superstitions and vulgar errors respecting 
the Sabbath. Second edition, with a large appendix. Lon- 
don, 12mo. 1833. This book was very heterodox at the 
time, but it has furnished material for some of the clergy 
of our day. 

I never could quite make out whether Godfrey Higgins 
took that system which he traced to the Buddhists to have 
a Divine origin, or to be the result of good men's medita- 
tions. Himself a strong theist, and believer in a future 



ON POPE'S DIPPING NEEDLE. 277 

state, one would suppose that he w,ould refer a universal 
religion, spread in different forms over the whole earth 
from one source, directly to the universal Parent. And this 
I suspect he did, whether he knew it or not. The external 
evidence is balanced. In his preface he says: 

"I cannot help smiling when I consider that the priests 
have objected to admit my former book, The Celtic Druids, 
into libraries, because it was antichristian ; and it has been 
attacked by Deists, because it was superfluously religious. 
The learned Deist, the Rev. R. Taylor [already mentioned], 
has designated me as the religious Mr. Higgins." 

The time will come when some profound historian of 
literature will make himself much clearer on the point than 
I am. 

ON POPE'S DIPPING NEEDLE. 

The triumphal Chariot of Friction: or a familiar elucidation of 
the origin of magnetic attraction, &c. &c. By William Pope. 1 
London, 1829, 4to. 

Part of this work is on a dipping-needle of the au- 
thor's construction. It must have been under the impression 
that a book of naval magnetism was proposed, that a 
great many officers, the Royal Naval Club, etc. lent their 
names to the subscription list. How must they have been 
surprised to find, right opposite to the list of subscribers, 
the plate presenting "the three emphatic letters, J. A. O." 
And how much more when they saw it set forth that if a 
square be inscribed in a circle, a circle within that, then a 
square again, &c., it is impossible to have more than fourteen 
circles, let the first circle be as large as you please. From 
this the seven attributes of God are unfolded ; and further, 
that all matter was moral, until Lucifer churned it into 
physical "as far as the third circle in Deity": this Lucifer, 
called Leviathan in Job, being thus the moving cause of 

1 He seems to have written nothing else. 



278 A BUDGET OF PARADOXES. 

chaos. I shall say no more, except that the friction of the 
air is the cause of magnetism. 

Remarks on the Architecture, Sculpture, and Zodiac of Pal- 
myra; with a Key to the Inscriptions. By B. Prescot. 2 Lon- 
don, 1830, 8vo. 

Mr. Prescot gives the signs of the zodiac a Hebrew 
origin. 

THE JACOTOT METHOD. 

Epitome de mathematiques. Par F. Jacotot, 1 Avocat. 3ieme 

edition, Paris, 1830, 8vo. (pp. 18). 
Methode Jacotot. Choix de propositions mathematiques. Par 

P. Y. Sepres. 2 2nde edition. Paris, 1830, 8vo. (pp. 82). 

Of Jacotot's method, which had some vogue in Paris, 
the principle was Tout est dans tout, 3 and the process Ap- 
prendre quelque chose, et a y rapporter tout le rested The 
first tract has a proposition in conic sections and its prelim- 
inaries: the second has twenty exercises, of which the first 
is finding the greatest common measure of two numbers, 
and the last is the motion of a point on a surface, acted on 
by given forces. This is topped up with the problem of 
sound in a tube, and a slice of Laplace's theory of the 
tides. All to be studied until known by heart, and all the 
rest will come, or at least join on easily when it comes. 
There is much truth in the assertion that new knowledge 

* See note I on page 270. The name is here spelled correctly. 

1 Joseph Jacotot (1770-1840), the father of this Fortune Jacotot, 
was an infant prodigy. At nineteen he was made professor of the 
humanities at Dijon. He served in the army, and then became pro- 
fessor of mathematics at Dijon. He continued in his chair until 
the restoration of the Bourbons, and then fled to Louvain. It was 
here that he developed the method with which his name is usually 
connected. He wrote a Mathematiques in 1827, which went through 
four editions. The Epitome is by his son, Fortune. 

* He wrote on educational topics and a Sacred History that went 
through several editions. 

' "All is in all." 

4 "Know one thing and refer everything else to it," as it is often 
translated. 



A DISCOURSE ON PROBABILITY. 279 

hooks on easily to a little of the old, thoroughly mastered. 
The day is coming when it will be found out that crammed 
erudition, got up for examinations, does not cast out any 
hooks for more. 

Lettre a MM. les Membres de 1' Academic Royale des Sciences, 
contenant un developpement de la refutation du systeme de la 
gravitation universelle, qui leur a ete presentee le 30 aout, 1830. 
Par Felix Passot 5 Paris, 1830, 8vo. 

Works of this sort are less common in France than in 
England. In France there is only the Academy of Sciences 
to go to: in England there is a reading public out of the 
Royal Society, &c. 

A DISCOURSE ON PROBABILITY. 

About 1830 was published, in the Library of Useful 
Knowledge, the tract on Probability, the joint work of the 
late Sir John Lubbock 1 and Mr. Drinkwater (Bethune). 2 
It is one of the best elementary openings of the subject. 
A binder put my name on the outside (the work was anon- 
ymous) and the consequence was that nothing could drive 
out of people's heads that it was written by me. I do 
not know how many denials I have made, from a passage 
in one of my own works to a letter in the Times : and I am 
not sure that I have succeeded in establishing the truth, 
even now. I accordingly note the fact once more. But 
as a book has no right here unless it contain a paradox 
or thing counter to general opinion or practice I will pro- 
duce two small ones. Sir John Lubbock, with whom lay 
the executive arrangement, had a strong objection to the 
last word in "Theory of Probabilities," he maintained that 
the singular probability, should be used; and I hold him 
quite right. 

5 A writer of no reputation. 

*Sir John Lubbock (1803-1865), banker, scientist, publicist, as- 
tronomer, one of the versatile men of his time. 
2 See note 8, page 99. 



280 A BUDGET OF PARADOXES. 

The second case was this: My friend Sir J. L., with a 
large cluster of intellectual qualities, and another of social 
qualities, had one point of character which I will not call 
bad and cannot call good ; he never used a slang expression. 
To such a length did he carry his dislike, that he could not 
bear head and tail, even in a work on games of chance: so 
he used obverse and reverse. I stared when I first saw 
this: but, to my delight, I found that the force of circum- 
stances beat him at last. He was obliged to take an example 
from the race-course, and the name of one of the horses 
was Bessy Bedlam I And he did not put her down as 
Elisabeth Bethlehem, but forced himself to follow the 
jockeys. 

[Almanach Remain sur la Loterie Royale de France, ou les 
Etrennes necessaires aux Actionnaires et Receveurs de la 
dite Loterie. Par M. Menut de St.-Mesmin. Paris, 1830. 
I2mo. 

This book contains all the drawings of the French lot- 
tery (two or three, each month) from 1758 to 1830. It is 
intended for those who thought they could predict the 
future drawings from the past: and various sets of sympa- 
thetic numbers are given to help them. The principle is, 
that anything which has not happened for a long time must 
be soon to come. At rouge et noir, for example, when the red 
has won five times running, sagacious gamblers stake on the 
black, for they think the turn which must come at last is 
nearer than it was. So it is: but observation would have 
shown that if a large number of those cases had been 
registered which show a run of five for the red, the next 
game would just as often have made the run into six as 
have turned in favor of the black. But the gambling rea- 
soner is incorrigible: if he would but take to squaring the 
circle, what a load of misery would be saved. A writer of 
1823, who appeared to be thoroughly acquainted with the 
gambling of Paris and London, says that the gamesters by 



A DISCOURSE ON PROBABILITY. 281 

profession are haunted by a secret foreboding of their future 
destruction, and seem as if they said to the banker at the 
table, as the gladiators said to the emperor, Morituri te 
salutant. 8 

In the French lottery, five numbers out of ninety were 
drawn at a time. Any person, in any part of the country, 
might stake any sum upon any event he pleased, as that 
27 should be drawn ; that 42 and 81 should be drawn ; that 
42 and 81 should be drawn, and 42 first; and so on up to 
a quine determine, if he chose, which is betting on five 
given numbers in a given order. Thus, in July, 1821, one 
of the drawings was 

8 46 16 64 13. 

A gambler had actually predicted the five numbers (but not 
their order), and won 131,350 francs on a trifling stake. M. 
Menut seems to insinuate that the hint what numbers to 
choose was given at his own office. Another won 20,852 
francs on the quaterne, 8, 16, 46, 64, in this very drawing. 
These gains, of course, were widely advertised : of the mul- 
titudes who lost nothing was said. The enormous number 
of those who played is proved to all who have studied 
chances arithmetically by the numbers of simple quaternes 
which were gained: in 1822, fourteen; in 1823, six; in 
1824, sixteen; in 1825, nine, &c. 

The paradoxes of what is called chance, or hazard, might 
themselves make a small volume. All the world under- 
stands that there is a long run, a general average ; but great 
part of the world is surprised that this general average 
should be computed and predicted. There are many re- 
markable cases of verification; and one of them relates to 
the quadrature of the circle. I give some account of this and 
another. Throw a penny time after time until head arrives, 
which it will do before long: let this be called a set. Ac- 
cordingly, H is the smallest set, TH the next smallest, then 
TTH, &c. For abbreviation, let a set in which seven tails 

'"Those about to die salute you." 



282 A BUDGET OF PARADOXES. 

occur before head turns up be T 7 H. In an immense num- 
ber of trials of sets, about half will be H ; about a quarter 
TH ; about an eighth, T 2 H. Buffon 4 tried 2,048 sets ; and 
several have followed him. It will tend to illustrate the 
principle if I give all the results ; namely, that many trials 
will with moral certainty show an approach and the greater 
the greater the number of trials to that average which 
sober reasoning predicts. In the first column is the most 
likely number of the theory : the next column gives Buffon's 
result; the three next are results obtained from trial by 

H . 1,024 . 1,061 . 1,048 . 1,017 . 1,039 

TH . 512 . 494 . 507 . 547 . 480 

T*H . 256 . 232 . 248 . 235 . 267 

T3H . 128 . 137 . 99 , 118 . 126 

T4H . 64 . 56 . 71 . 72 . 67 

TsH . 32 . 29 . 38 . 32 . 33 

T 6 H . 16 . 25 . 17 . 10 . 19 

T7H . 8 . 8 . 9 . 9 . 10 

T 8 H . 4 . 6 . 5 . 3 . 3 

T9H 2 . 3.2.4 

T'H 1 . 1.1 

T"H . 1 

T"H . 

T'3H 1 . 1.0 

T'4H 

T'sH 1 . 1 

&c. 0.0 

2,048 . 2,048 . 2,048 . 2,048 . 2,048 

4 Georges Louis Leclerc Buffon (1707-1788), the well-known 
biologist. He also experimented with burning mirrors, his results 
appearing in his Invention des miroirs ardens pour bruler a une 
grande distance (1747). The reference here may be to his Resolu- 
tion des problemes qui re gar dent le jeu du franc carreau (1733). 
The prominence of his Histoire naturelle (36 volumes, 1749-1788) 
has^ overshadowed the credit due to him for his translation of New- 
ton's work on Fluxions. 



A DISCOURSE ON PROBABILITY. 283 

correspondents of mine. In each case the number of trials 
is 2,048. 

In very many trials, then, we may depend upon something 
like the predicted average. Conversely, from many trials 
we may form a guess at what the average will be. Thus, 
in Buffon's experiment the 2,048 first throws of the sets 
gave head in 1,061 cases: we have a right to infer that in 
the long run something like 1,061 out of 2,048 is the pro- 
portion of heads, even before we know the reasons for the 
equality of chance, which tell us that 1,024 out of 2,048 is 
the real truth. I now come to the way in which such con- 
siderations have led to a mode in which mere pitch-and-toss 
has given a more accurate approach to the quadrature of the 
circle than has been reached by some of my paradoxers. 
What would my friend 5 in No. 14 have said to this? The 
method is as follows: Suppose a planked "floor of the usual 
kind, with thin visible seams between the planks. Let there 
be a thin straight rod, or wire, not so long as the breadth of 
the plank. This rod, being tossed up at hazard, will either 
fall quite clear of the seams, or will lay across one seam. 
Now Buffon, and after him Laplace, proved the following: 
That in the long run the fraction of the whole number of 
trials in which a seam is intersected will be the fraction 
which twice the length of the rod is of the circumference 
of the circle having the breadth of a plank for its diameter. 
In 1855 Mr. Ambrose Smith, of Aberdeen, made 3,204 
trials with a rod three-fifths of the distance between the 
planks: there were 1,213 clear intersections, and 11 contacts 
on which it was difficult to decide. Divide these contacts 
equally, and we have 1,218J to 3,204 for the ratio of 6 to 
5?r, presuming that the greatness of the number of trials 
gives something near to the final average, or result in the 
long run: this gives 7r = 3.1553. If all the 11 contacts had 
been treated as intersections, the result would have been 

5 See page 285. This article was a supplement to No. 14 in the 
Athenaum Budget. A. De M. 



284 A BUDGET OF PARADOXES. 

7r = 3.1412, exceedingly near. A pupil of mine made 600 
trials with a rod of the length between the seams, and got 
7r = 3.137. 

This method will hardly be believed until it has been 
repeated so often that "there never could have been any 
doubt about it." 

The first experiment strongly illustrates a truth of the 
theory, well confirmed by practice: whatever can happen 
will happen if we make trials enough. Who would under- 
take to throw tail eight times running? Nevertheless, in 
the 8,192 sets tail 8 times running occurred 17 times; 9 
times running, 9 times; 10 times running, twice; 11 times 
and 13 times, each once; and 15 times twice.] 

ON CURIOSITIES OF . 

1830. The celebrated interminable fraction 3. 14159. 
which the mathematician calls TT, is the ratio of the circum- 
ference to the diameter. But it is thousands of things 
besides. It is constantly turning up in mathematics : and if 
arithmetic and algebra had been studied without geometry, 
TT must have come in somehow, though at what stage or 
under what name must have depended upon the casualties 
of algebraical invention. This will readily be seen when 
it is stated that TT is nothing but four times the series 

l- 1 /3 + 1 /5- 1 /7 + 1 /9- 1 /ll+.... 

ad infinitum. 1 It would be wonderful if so simple a series 



are many similar series and products. Among the more 
interesting are the following: 

7r_2-2-4-4-6-6-8... 
2 1-3-3-5-5-7-7... ' 

I rz ~ ~ ~""~ * 



t 2-3-4 4-5-6 6-7-8 

"6 ~~ \ 3" \ 8*3 y S S^7- S* -t"" / ' 

=t(i L+_I L+. . . WJL. 

4 \ 5 3*5^ 5 "5** 7'5 7 / \23Q 



ON CURIOSITIES OF TT. 285 

had but one kind of occurrence. As it is, our trigonometry 
being founded on the circle, IT first appears as the ratio 
stated. If, for instance, a deep study of probable fluctua- 
tion from average had preceded, TT might have emerged as 
a number perfectly indispensable in such problems as : What 
is the chance of the number of aces lying between a million 
+ x and a million - x, when six million of throws are made 
with a die? I have not gone into any detail of all those 
cases in which the paradoxer finds out, by his unassisted 
acumen, that results of mathematical investigation cannot 
be : in fact, this discovery is only an accompaniment, though 
a necessary one, of his paradoxical statement of that which 
must be. Logicians are beginning to see that the notion 
of horse is inseparably connected with that of non-horse: 
that the first without the second would be no notion at all. 
And it is clear that the positive affirmation of that which 
contradicts mathematical demonstration cannot but be ac- 
companied by a declaration, mostly overtly made, that dem- 
onstration is false. If the mathematician were interested 
in punishing this indiscretion, he could make his denier 
ridiculous by inventing asserted results which would com- 
pletely take him in. 

More than thirty years ago I had a friend, now long 
gone, who was a mathematician, but not of the higher 
branches: he was, inter alia, thoroughly up in all that 
relates to mortality, life assurance, &c. One day, explain- 
ing to him how it should be ascertained what the chance 
is of the survivors of a large number of persons now alive 
lying between given limits of number at the end of a certain 
time, I came, of course upon the introduction of IT, which 
I could only describe as the ratio of the circumference of 
a circle to its diameter. "Oh, my dear friend ! that must be 
a delusion ; what can the circle have to do with the numbers 
alive at the end of a given time?" "I cannot demonstrate 
it to you ; but it is demonstrated." "Oh ! stuff ! I think you 
can prove anything with your differential calculus : figment, 



286 A BUDGET OF PARADOXES. 

depend upon it." I said no more; but, a few days after- 
wards, I went to him and very gravely told him that I had 
discovered the law of human mortality in the Carlisle Table, 
of which he thought very highly. I told him that the law 
was involved in this circumstance. Take the table of ex- 
pectation of life, choose any age, take its expectation and 
make the nearest integer a new age, do the same with that, 
and so on; begin at what age you like, you are sure to 
end at the place where the age past is equal, or most nearly 
equal, to the expectation to come. "You don't mean that 
this always happens?" "Try it." He did try, again and 
again; and found it as I said. "This is, indeed, a curious 
thing; this is a discovery." I might have sent him about 
trumpeting the law of life : but I contented myself with in- , 
forming him that the, same thing would happen with any 
table whatsoever in which the first column goes up and 
the second goes down ; and that if a proficient in the higher 
mathematics chose to palm a figment upon him, he could 
do without the circle : a corsair e } corsair e et demi? the French 
proverb says. "Oh!" it was remarked, "I see, this was 
Milne !" 3 It was not Milne : I remember well showing the 
formula to him some time afterwards. He raised no diffi- 
culty about ?r; he knew the forms of Laplace's results, and 
he was much interested. Besides, Milne never said stuff! 
and figment! And he would not have been taken in: he 
would have quietly tried it with the Northampton and all 
the other tables, and would have got at the truth. 

8 "To a privateer, a privateer and a half." 

3 Joshua Milne (1776-1851) was actuary of the Sun Life Assur- 
ance Society. He wrote A Treatise on the Valuation of Annuities 
and Assurances on Lives and Survivorships; on the Construction 
of tables of mortality; and on the Probabilities and Expectations of 
Life, London, 1815. Upon the basis of the Carlisle bills of mortality 
of Dr. Heysham he reconstructed the mortality tables then in use 
and which were based upon the Northampton table of Dr. Price. His 
work revolutionized the actuarial science of the time. In later years 
he devoted his attention to natural history. 



EUCLID WITHOUT AXIOMS. 287 

EUCLID WITHOUT AXIOMS. 

The first book of Euclid's Elements. With alterations and 
familiar notes. Being an attempt to get rid of axioms alto- 
gether; and to establish the theory of parallel lines, without 
the introduction of any principle not common to other parts of 
the elements. By a member of the University of Cambridge. 
Third edition. In usum serenissimae filiolse. London, 1830. 

The author was Lieut. Col. (now General) Perronet 
Thompson, 1 the author of the "Catechism on the Corn 
Laws." I reviewed the fourth edition which had the name 
of "Geometry without Axioms," 1833 in the quarterly 
Journal of Education for January, 1834. Col. Thompson, 
who then was a contributor to if not editor of the West- 
minster Review, replied in an article the authorship of which 
could not be mistaken. 

Some more attempts upon the problem, by the same 
author, will be found in the sequel. They are all of acute 
and legitimate speculation; but they do not conquer the 
difficulty in the manner demanded by the conditions of the 
problem. The paradox of parallels does not contribute 
much to my pages: its cases are to be found for the most 
part in geometrical systems, or in notes to them. Most of 
them consist in the proposal of additional postulates ; some 
are attempts to do without any new postulate. Gen. Perronet 
Thompson, whose paradoxes are always constructed on 
much study of previous writers, has collected in the work 
above named, a budget of attempts, the heads of which 
are in the Penny and English Cyclopedias, at "Parallels." 
He has given thirty instances, selected from what he had 
found. 2 

1 See note 2, page 252. He also wrote the Theory of Parallels. 
The proof of Euclid's axiom looked for in the properties of the 
equiangular spiral (London, 1840), which went through four edi- 
tions, and the Theory of Parallels. The proof that the three angles 
of a triangle are equal to two right angles looked for in the inflation 
of the sphere (London, 1853), of which there were three editions. 

2 For the latest summary, see W. B. Frankland, Theories of 
Parallelism, an historical critique, Cambridge, 1910. 



288 A BUDGET OF PARADOXES. 

Lagrange, 3 in one of the later years of his life, imag- 
ined that he had overcome the difficulty. He went so far 
as to write a paper, which he took with him to the Insti- 
tute, and began to read it. But in the first paragraph some- 
thing struck him which he had not observed: he muttered 
// faut que j'y songe encore* and put the paper in his 
pocket. 



THE LUNAR CAUSTIC JOKE. 

The following paragraph appeared in the Morning Post, 
May 4, 1831 : 

"We understand that although, owing to circumstances 
with which the public are not concerned, Mr. Goulburn 1 
declined becoming a candidate for University honors, that 
his scientific attainments are far from inconsiderable. He 
is well known to be the author of an essay in the Philosoph- 
ical Transactions on the accurate rectification of a circular 
arc, and of an investigation of the equation of a lunar 
caustic a problem likely to become of great use in nautical 
astronomy." 

'Joseph Louis Lagrange (1736-1813), author of the Mecanique 
analytique (1788), Theorie des fonctions analytiques (1797), Traite 
de la resolution des equations numeriques de tous degres (1798), 
Leqons sur le calcul des fonctions (1806), and many memoirs. Al- 
though born in Turin and spending twenty of his best years in Ger- 
many, he is commonly looked upon as the great leader of French 
mathematicians. The last twenty-seven years of his life were spent in 
Paris, and his remarkable productivity continued to the time of his 
death. His genius in the theory of numbers was probably never ex- 
celled except by Fermat He received very high honors at the hands 
of Napoleon and was on the first staff of the Ecole polytechnique 
(1797). 

4 "I shall have to think it over again." 

1 Henry Goulburn (1784-1856^ held various government posts. 
He was under-secretary for war and the colonies (1813), commis- 
sioner to negotiate peace with America (1814), chief secretary to 
the Lord Lieutenant of Ireland (1821), and several times Chancellor 
of the Exchequer. On the occasion mentioned by De Morgan he 
was standing for parliament, and was successful. 



THE LUNAR CAUSTIC JOKE. 289 

This hoax which would probably have succeeded with 
any journal was palmed upon the Morning Post, which 
supported Mr. Goulburn, by some Cambridge wags who sup- 
ported Mr. Lubbock, the other candidate for the University 
of Cambridge. Putting on the usual concealment, I may 
say that I always suspected Dr-nkw-t-r B-th-n- 2 of having 
a share in the matter. The skill of the hoax lies in avoiding 
the words "quadrature of the circle," which all know, and 
speaking of "the accurate rectification of a circular arc," 
which all do not know for its synonyme. The Morning 
Post next day gave a reproof to hoaxers in general, without 
referring to any particular case. It must be added, that 
although there are caustics in mathematics, there is no 
lunar caustic. 

So far as Mr. Goulburn was concerned, the above was 
poetic justice. He was the minister who, in old time, told 
a deputation from the Astronomical Society that the Gov- 
ernment "did not care twopence for all the science in the 
country." There may be some still alive who remember 
this: I heard it from more than one of those who were 
present, and are now gone. Matters are much changed. 
I was thirty years in office at the Astronomical Society ; 
and, to my certain knowledge, every Government of that 
period, Whig and Tory, showed itself ready to help with 
influence when wanted, and with money whenever there 
was an answer for the House of Commons. The following 
correction subsequently appeared. Referring to the hoax 
about Mr. Goulburn, Messrs. C. H. and Thompson Cooper 8 
have corrected an error, by stating that the election which 
gave rise to the hoax was that in which Messrs. Goulburn 

2 On Drinkwater Bethtme see note 8, page 99. 

"Charles Henry Cooper (1808-1866) was a biographer and an- 
tiquary. He was town clerk of Cambridge (1849-1866) and wrote 
the Annals of Cambridge (1842-1853). His Memorials of Cam- 
bridge (1874) appeared after his death. Thompson Cooper was his 
son, and the two collaborated in the Athenae Cantabrigiewis (1858). 



290 A BUDGET OF PARADOXES. 

and Yates Peel 4 defeated Lord Palmerston 5 and Mr. Caven- 
dish. 6 They add that Mr. Gunning, the well-known Es- 
quire Bedell of the University, attributed the hoax to the 
late Rev. R. Sheepshanks, to whom, they state, are also 
attributed certain clever fictitious biographies of public 
men, as I understand it which were palmed upon the edi- 
tor of the Cambridge Chronicle, who never suspected their 
genuineness to the day of his death. Being in most confi- 
dential intercourse with Mr. Sheepshanks, 7 both at the time 
and all the rest of his life (twenty-five years), and never 
heard him allude to any such things which were not in 
his line, though he had satirical power of quite another 

* William Yates Peel (1789-1858) was a brother of Sir Robert 
Peel, he whose name degenerated into the familiar title of the 
London "Bobby" or "Peeler." Yates Peel was a member of parliament 
almost continuously from 1817 to 1852. He represented Cambridge 
at Westminster from 1831 to 1835. 

5 Henry John Temple, third Viscount of Palmerston (1784-1865), 
was member for Cambridge in 1811, 1818, 1820, 1826 (defeating 
Goulburn), and 1830. He failed of reelection in 1831 because of his 
advocacy of reform. This must have been the time when Goulburn 
defeated him. He was Foreign Secretary (1827) and Secretary of 
State for Foreign Affairs (1830-1841, and 1846-1851). It is said of 
him that he "created Belgium, saved Portugal and Spain from ab- 
solutism, rescued Turkey from Russia and the highway to India from 
France." He was Prime Minister almost continuously from 1855 to 
1865, a period covering the Indian Mutiny and the American Civil 
War. 

'William Cavendish, seventh Duke of Devonshire (1808-1891). 
He was member for Cambridge from 1829 to 1831, but was defeated 
in 1831 because he had favored parliamentary reform. He became 
Earl of Burlington in 1834, and Duke of Devonshire in 1858. He was 
much interested in the promotion of railroads and in the iron and 
steel industries 

'Richard Sheepshanks (1794-1855) was a brother of John Sheep- 
shanks the benefactor of art. (See note 3, p. 147.) He was a fellow of 
Trinity College, Cambridge, a fellow of the Royal Society and secretary 
of the Astronomical Society. Babbage (See note 12, p. 207) suspected 
him of advising against the government support of his calculating 
machine and attacked him severely in his Exposition of 1851, in the 
chapter on The Intrigues of Science. Babbage also showed that 
Sheepshanks got an astronomical instrument of French make through 
the custom house by having Troughton's (See note 2, page 152) name 
engraved on it. Sheepshanks admitted this second charge, but wrote 
a Letter in Reply to the Calumnies of Mr. Babbage, which was pub- 
lished in 1854. He had a. highly controversial nature. 



ON M. DEMONVILLE. 291 

kind I feel satisfied he had nothing to do with them. I 
may add that others, his nearest friends, and also members 
of his family, never heard him allude to these hoaxes as 
their author, and disbelieve his authorship as much as I 
do myself. I say this not as imputing any blame to the 
true author, such hoaxes being fair election jokes in all 
time, but merely to put the saddle off the wrong horse, and 
to give one more instance of the insecurity of imputed 
authorship. Had Mr. Sheepshanks ever told me that he 
had perpetrated the hoax, I should have had no hesitation 
in giving it to him. I consider all clever election squibs, 
free from bitterness and personal imputation, as giving the 
multitude good channels for the vent of feelings which 
but for them would certainly find bad ones. 

[But I now suspect that Mr. Babbage 8 had some hand 
in the hoax. He gives it in his "Passages, &c." and is evi- 
dently writing from memory, for he gives the wrong year. 
But he has given the paragraph, though not accurately, 
yet with such a recollection of the points as brings sus- 
picion of the authorship upon him, perhaps in conjunction 
with D. B. 9 Both were on Cavendish's committee. Mr. 
Babbage adds, that "late one evening a cab drove up in hot 
haste to the office of the Morning Post, delivered .the copy 
as coming from Mr. Goulburn's committee, and at the same 
time ordered fifty extra copies of the Post to be sent next 
morning to their committee-room. I think the man the 
only one I ever heard of who knew all about the cab and 
the extra copies must have known more.] 

ON M. DEMONVILLE. 

Demonville. A Frenchman's Christian name is his 
own secret, unless there be two of the surname. M. Demon- 
ville is a very good instance of the difference between a 

8 See note 12, page 207. The work referred to is Passages from 
the Life of a Philosopher, London, 1864. 

9 Drinkwater Bethune. See note 8, page 99. 



292 A BUDGET OF PARADOXES. 

French and English discoverer. In England there is a 
public to listen to discoveries in mathematical subjects made 
without mathematics : a public which will hear, and wonder, 
and think it possible that the pretensions of the discoverer 
have some foundation. The unnoticed man may possibly 
be right: and the old country-town reputation which I once 
heard of, attaching to a man who "had written a book 
about the signs of the zodiac which all the philosophers in 
London could not answer," is fame as far as it goes. Ac- 
cordingly, we have plenty of discoverers who, even in as- 
tronomy, pronounce the learned in error because of mathe- 
matics. In France, beyond the sphere of influence of the 
Academy of Sciences, there is no one to cast a thought 
upon the matter : all who take the least interest repose entire 
faith in the Institute. Hence the French discoverer turns 
all his thoughts to the Institute, and looks for his only 
hearing in that quarter. He therefore throws no slur upon 
the means of knowledge, but would say, with M. Demon- 
ville: "A 1'egard de M. Poisson, 1 j'envie loyalement la 
millieme partie de ses connaissances mathematiques, pour 
prouver mon systeme d'astronomie aux plus incredules." 2 
This system is that the only bodies of our system are the 
earth, the sun, and the moon ; all the others being illusions, 
caused by reflection of the sun and moon from the ice of 
the polar regions. In mathematics, addition and subtraction 
are for men; multiplication and division, which are in 
truth creation and destruction, are prerogatives of deity. 
But nothing multiplied by nothing is one. M. Demonville 
obtained an introduction to William the Fourth, who de- 
sired the opinion of the Royal Society upon his system : the 

1 Simeon-Denis Poisson (1781-1840) was professor of calculus 
and mechanics at the Ecole polytechnique. He was made a baron by 
Napoleon, and was raised to the peerage in 1837. His chief works 
are the Traite de mecanique (1811) and the Traite mathematique de 
la chaleur (1835). 

*"As to M. Poisson, I really wish I had a thousandth part of 
his mathematical knowledge that I might prove my system to the 
incredulous." 



PARSE Y^S PARADOX. 293 

answer was very brief. The King was quite right ; so was 
the Society: the fault lay with those who advised His 
Majesty on a matter they knew nothing about. The writ- 
ings of M. Demonville in my possession are as follows. 3 
The dates which were only on covers torn off in binding 
were about 1831-34: 

Petit cours d 'astronomic* followed by Sur I'unite mathe- 
matique. Principes de la physique de la creation implicite- 
ment admis dans la notice sur le tonnerre par M. Arago. 
Question de longitude sur mer.* Vrai systeme du monde Q 
(pp. 92). Same title, four pages, small type. Same title, 
four pages, addressed to the British Association. Same title, 
four pages, addressed to M. Mathieu. Same title, four 
pages, on M. Bouvard's report. Resume de la physique 
de la creation; troisieme par tie du vrai systeme du monde. 1 

PARSEY'S PARADOX. 

The quadrature of the circle discovered, by Arthur Parsey, 1 
author of the 'art of miniature painting/ Submitted to the 
consideration of the Royal Society, on whose protection the 
author humbly throws himself. London, 1832, 8vo. 

Mr. Parsey was an artist, who also made himself con- 
spicuous by a new view of perspective. Seeing that the 
sides of a tower, for instance, would appear to meet in a 
point if the tower were high enough, he thought that these 
sides ought to slope to one another in the picture. On this 

This list includes most of the works of Antoine-Louis-Guenard 
Demonville. There was also the Nouveau systeme du monde. ... et 
hypotheses conformes aux experiences sur les vents, sur la lumiere 
et sur le Huide electro-magnetique, Paris, 1830. 

'Paris, 1835. 
"Paris, 1833. 

c The second part appeared in 1837. There were also editions in 
1850 and 1852, and one edition appeared without date. 

1 Paris, 1842. 

1 Parsey also wrote The Art of Miniature Painting on Ivory 
(1831), Perspective Rectified (1836), and The Science of Vision 
(1840), the third being a revision of the second. 



294 A BUDGET OF PARADOXES. 

theory he published a small work, of which I have not the 
title, with a Grecian temple in the frontispiece, stated, if 
I remember rightly, to be the first picture which had ever 
been drawn in true perspective. Of course the building 
looked very Egyptian, with its sloping sides. The answer 
to his notion is easy enough. What is called the picture 
is not the picture from which the mind takes its perception ; 
that picture is on the retina. The intermediate picture, as it 
may be called the human artist's work is itself seen per- 
spectively. If the tower were so high that the sides, though 
parallel, appeared to meet in a point, the picture must also 
be so high that the picture-sides, though parallel, would ap- 
pear to meet in a point. I never saw this answer given, 
though I have seen and heard the remarks of artists on Mr. 
Parsey's work. I am inclined to think it is commonly sup- 
posed that the artist's picture is the representation which 
comes before the mind : this is not true ; we might as well 
say the same of the object itself. In July 1831, reading an 
article on squaring the circle, and finding that there was a 
difficulty, he set to work, got a light denied to all mathe- 
maticians in some would say through a crack, and ad- 
vertised in the Times that he had done the trick. He then 
prepared this work, in which, those who read it will see 

how, he showed that 3.14159 should be 3.0625. He 

might have found out his error by stepping a draughtsman's 
circle with the compasses. 

Perspective has not had many paradoxes. The only 
other one I remember is that of a writer on perspective, 
whose name I forget, and whose four pages I do not possess. 
He circulated remarks on my notes on the subject, pub- 
lished in the Athen&um, in which he denies that the stereo- 
graphic projection is a case of perspective, the reason 
being that the whole hemisphere makes too large a picture 
for the eye conveniently to grasp at once. That is to say, 
it is no perspective because there is too much perspective. 



ON A COUPLE OF GEOMETRIES. 295 



ON A COUPLE OF GEOMETRIES. 

Principles of Geometry familiarly illustrated. By the Rev. W. 

Ritchie, 1 LL.D. London, 1833, I2mo. 
A new Exposition of the system of Euclid's Elements, being an 

attempt to establish his work on a different basis. By Alfred 

Day, 2 LL.D. London, 1839, I2mo. 

These works belong to a small class which have the 
peculiarity of insisting that in the general propositions of 
geometry a proposition gives its converse: that "Every B 
is A" follows from "Every A is B." Dr. Ritchie says, "If it 
be proved that the equality of two of the angles of a triangle 
depends essentially upon the equality of the opposite sides, 
it follows that the equality of opposite sides depends essen- 
tially on the equality of the angles." Dr. Day puts it as 
follows : 

"That the converses of Euclid, so called, where no par- 
ticular limitation is specified or implied in the leading prop- 
osition, more than in the converse, must be necessarily true ; 
for as by the nature of the reasoning the leading proposition 
must be universally true, should the converse be not so, it 
cannot be so universally, but has at least all the exceptions 
conveyed in the leading proposition, and the case is there- 
fore unadapted to geometric reasoning; or, what is the 
same thing, by the very nature of geometric reasoning, the 
particular exceptions to the extended converse must be 
identical with some one or other of the cases under the 
universal affirmative proposition with which we set forth, 
which is absurd." 

1 William Ritchie (1790-1837) was a physicist who had studied 
at Paris under Biot and Gay-Lussac. He contributed several papers 
on electricity, heat, and elasticity, and was looked upon as a good 
experimenter. Besides the geometry he wrote the Principles of the 
Differential and Integral Calculus (1836). 

2 Alfred Day (1810-1849) was a man who was about fifty years 
ahead of his time in his attempt to get at the logical foundations of 
geometry. It is true that he laid himself open to criticism, but his 
work was by no means bad. He also wrote A Treatise on Harmony 
(1849, second edition 1885), The Rotation of the Pendulum (1851), 
and several works on Greek and Latin Grammar. 



296 A BUDGET OF PARADOXES. 

On this I cannot help transferring to my reader the 
words of the Pacha when he orders the bastinado, May 
it do you good ! A rational study of logic is much wanted 
to show many mathematicians, of all degrees of proficiency, 
that there is nothing in the reasoning of mathematics which 
differs from other reasoning. Dr. Day repeated his argu- 
ment in A Treatise on Proportion, London, 1840, 8vo. Dr. 
Ritchie was a very clear-headed man. He published, in 
1818, a work on arithmetic, with rational explanations. , 
This was too early for such an improvement, and nearly 
the whole of his excellent work was sold as waste paper. 
His elementary introduction to the Differential Calculus 
was drawn up while he was learning the subject late in 
life. Books of this sort are often very effective on points 
of difficulty. 

NEWTON AGAIN OBLITERATED. 

Letter to the Royal Astronomical Society in refutation of Mis- 
taken Notions held in common, by the Society, and by all 
the Newtonian philosophers. By Capt. Forman, 1 R.N. Shep- 
ton-Mallet, 1833, 8vo. 

Capt. Forman wrote against the whole system of gravi- 
tation, and got no notice. He then wrote to Lord Brougham, 
Sir J. Herschel, and others I suppose, desiring them to 
procure notice of his books in the reviews: this not being 
acceded to, he wrote (in print) to Lord John Russell 2 to 
complain of their "dishonest" conduct. He then sent a 
manuscript letter to the Astronomical Society, inviting con- 
troversy: he was answered by a recommendation to study 

1 Walter Forman wrote a number of controversial tracts. His 
first seems to have been A plan for improving the Revenue without 
adding to the burdens of the people, a letter to Canning in 1813. He 
also wrote A New Theory of the Tides (1822). His Letter to Lord 
John Russell, on Lord Brougham's most extraordinary conduct; and 
another to Sir J. Herschel, on the application of Kepler's third law 
appeared in 1832. 

8 Lord John Russell (1792-1878)' first Earl Russell, was one of 
the strongest supporters of the reform measures of the early Vic- 
torian period. He became prime minister in 1847, and again in 1865. 



NEWTON AGAIN OBLITERATED. 297 

dynamics. The above pamphlet was the consequence, in 
which, calling the Council of the Society "craven dunghill 
cocks," he set them right about their doctrines. From all 
I can learn, the life of a worthy man and a creditable officer 
was completely embittered by his want of power to see that 
no person is bound in reason to enter into controversy 
with every one who chooses to invite him to the field. This 
mistake is not peculiar to philosophers, whether of ortho- 
doxy or paradoxy; a majority of educated persons imply, 
by their modes of proceeding, that no one has a right to 
any opinion which he is not prepared to defend against all 
comers. 

David and Goliath, or an attempt to prove that the Newtonian 
system of Astronomy is directly opposed to the Scriptures. 
By Wm. Lauder, 1 Sen., Mere, Wilts. Mere, 1833, I2mo. 

Newton is Goliath; Mr. Lauder is David. David took 
five pebbles ; Mr. Lauder takes five arguments. He expects 
opposition ; for Paul and Jesus both met with it. 

Mr. Lauder, in his comparison, seems to put himself in 
the divinely inspired class. This would not be a fair in- 
ference in every case ; but we know not what to think when 
we remember that a tolerable number of cyclometers have 
attributed their knowledge to direct revelation. The works 
of this class are very scarce ; I can only mention one or two 
from Montucla. 2 Alphonso Cano de Molina, 3 in the last 
century, upset all Euclid, and squared the circle upon the 
ruins ; he found a follower, Janson, who translated him from 
Spanish into Latin. He declared that he believed in Euclid, 
until God, who humbles the proud, taught him better. One 
Paul Yvon, called from his estate de la Leu, a merchant at 
Rochelle, supported by his book-keeper, M. Pujos, and a 

1 Lauder seems never to have written anything else. 

2 See note i, page 40. 

3 The names of Alphonso Cano de Molina, Yvon, and Robert 
Sara have no standing in the history of the subject beyond what 
would be inferred from De Morgan's remark. 



298 A BUDGET OF PARADOXES. 

Scotchman, John Dunbar, solved the problem by divine 
grace, in a manner which was to convert all Jews, Infidels, 
etc. There seem to have been editions of his work in 1619 
and 1628, and a controversial "Examen" in 1630, by Robert 
Sara. There was a noted discussion, in which Mydorge, 4 
Hardy, 5 and others took part against de la Leu. I cannot 
find this name either in Lipenius 6 or Murhard, 7 and I 
should not have known the dates if it had not been for 
one of the keenest bibliographers of any time, my friend 
Prince Balthasar Boncompagni, 8 who is trying to find copies 
of the works, and has managed to find copies of the titles. 
In 1750, Henry Sullamar, an Englishman, squared the circle 
by the number of the Beast: he published a pamphlet every 
two or three years ; but I cannot find any mention of him in 
English works. 9 In France, in 1753, M. de Causans, 10 of 
the Guards, cut a circular piece of turf, squared it, and 

4 Claude Mydorge (1585-1647), an intimate friend of Descartes, 
was a dilletante in mathematics who read much but accomplished 
little. His Recreations mathematiques is his chief work. Boncom- 
pagni published the "Problemes de Mydorge" in his Bulletino. 

6 Claude Hardy was born towards the end of the i6th century 
and died at Paris in 1678. In 1625 he edited the Data Euclidis, 
publishing the Greek text with a Latin translation. He was a friend 
of Mydorge and Descartes, but an opponent of Fermat. 

6 That is, in the Bibliotheca Realis of Martin Lipen, or Lipenius 
(1630-1692), which appeared in six folio volumes, at Frankfort, 
1675-1685. 

7 See note 4, page 43. 

8 Baldassare Boncompagni (1821-1894) was the greatest general 
collector of mathematical works that ever lived, possibly excepting 
Libri. His magnificent library was dispersed at his death. His 
Bulletino (1868-1887) is one of the greatest source books on the 
history of mathematics that we have. He also edited the works of 
Leonardo of Pisa. 

9 He seems to have attracted no attention since De Morgan's 
search, for he is not mentioned in recent bibliographies. 

10 Joseph-Louis Vincens de Mouleon de Causans was born about 
the beginning of the i8th century. He was a Knight of Malta, 
colonel in the infantry, prince of Conti, and governor of the princi- 
pality of Orange. His works on geometry are the Prospectus apolo- 
getique pour la quadrature du cercle (1753), and La vraie geometrie 
transcendante (1754). 



SIR JOHN HERSCHEL. 299 

deduced original sin and the Trinity. He found out that 
the circle was equal to the square in which it is inscribed; 
and he offered a reward for detection of any error, and 
actually deposited 10,000 francs as earnest of 300,000. But 
the courts would not allow any one to recover. 

SIR JOHN HERSCHEL. 

1834. In this year Sir John Herschel 1 set up his tel- 
escope at Feldhausen, Cape of Good Hope. He did much 
for astronomy, but not much for the Budget of Paradoxes. 
He gives me, however, the following story. He showed a 
resident a remarkable blood-red star, and some little time 
after he heard of a sermon preached in those parts in which 
it was asserted that the statements of the Bible must be 
true, for that Sir J. H. had seen in his telescope "the very 
place where wicked people go." 

But red is not always the color. Sir J. Herschel has in 
his possession a letter written to his father, Sir W. H., 2 
dated April 3, 1787, and signed "Eliza Cumyns," begging 
to know if any of the stars be indigo in color, "because, if 
there be, I think it may be deemed a strong conjectural illus- 
tration of the expression, so often used by our Saviour in 
the Holy Gospels, that 'the disobedient shall be cast into 
outer darkness' ; for as the Almighty Being can doubtless 
confine any of his creatures, whether corporeal or spiritual, 
to what part of his creation He pleases, if therefore any of 
the stars (which are beyond all doubt so many suns to 
other systems) be of so dark a color as that above men- 
tioned, they may be calculated to give the most insufferable 
heat to those dolorous systems dependent upon them (and 
to reprobate spirits placed there) , without one ray of cheer- 
ful light ; and may therefore be the scenes of future punish- 
ments." This letter is addressed to Dr. Heirschel at Slow. 
Some have placed the infernal regions inside the earth, but 

1 See note 5, page 80. 

2 See note 6, page 81. 



300 A BUDGET OF PARADOXES. 

others have filled this internal cavity for cavity they will 
have with refulgent light, and made it the abode of the 
blessed. It is difficult to build without knowing the num- 
ber to be provided for. A friend of mine heard the follow- 
ing (part) dialogue between two strong Scotch Calvinists: 
"Noo! hoo manny d'ye thank there are of the alact on the 
arth at this moment? Eh! mabbee a doozen Hoot! mon! 
nae so mony as thot !" 

THE NAUTICAL ALMANAC. 

1834. From 1769 to 1834 the Nautical Almanac was 
published on a plan which gradually fell behind what was 
wanted. In 1834 the new series began, under a new super- 
intendent (Lieut. W. S. Stratford). 1 There had been a long 
scientific controversy, which would not be generally in- 
telligible. To set some of the points before the reader, I 
reprint a cutting which I have by me. It is from the 
Nautical Magazine, but I did hear that some had an idea 
that it was in the Nautical Almanac itself. It certainly was 
not, and I feel satisfied the Lords of the Admiralty would 
not have permitted the insertion ; they are never in advance 
of their age. The Almanac for 1834 was published in July 
1833. 

THE NEW NAUTICAL ALMANAC Extract from the Trimum 
Mobile/ and 'Milky Way Gazette/ Communicated by AERO- 
LITH. 

A meeting of the different bodies composing the Solar 
System was this day held at the Dragon's Tail, for the 
purpose of taking into consideration the alterations and 
amendments introduced into the New Nautical Almanac. 
The honorable luminaries had been individually summoned 

1 Lieut. William Samuel Stratford (1791-1853), was in active 
service during the Napoleonic wars but retired from the army in 
1815. He was first secretary of the Astronomical Society (1820) 
and became superintendent of the Nautical Almanac in 1831. With 
Francis Baily he compiled a star catalogue, and wrote on Halley's 
(1835-1836) and Encke's (1838) comets. 



THE NAUTICAL ALMANACK. 301 

by fast-sailing comets, and there was a remarkably full at- 
tendance. Among the visitors we observed several nebulae, 
and almost all the stars whose proper motions would admit 
of their being present. 

The SUN was unanimously called to the focus. The 
small planets took the oaths, and their places, after a short 
discussion, in which it was decided that the places should 
be those of the Almanac itself, with leave reserved to move 
for corrections. 

Petitions were presented from a and 8 Ursae Minoris, 
complaining of being put on daily duty, and praying for 
an increase of salary. Laid on the plane of the ecliptic. 

The trustees of the eccentricity 2 and inclination funds 
reported a balance of .00001 in the former, and a deficit 
of 0".009 in the latter. This announcement caused con- 
siderable surprise, and a committee was moved for, to as- 
certain which of the bodies had more or less than his share. 
After some discussion, in which the small planets offered 
to consent to a reduction, if necessary, the motion was 
carried. 

The FOCAL BODY then rose to address the meeting. He 
remarked that the subject on which they were assembled 
was one of great importance to the routes and revolutions 
of the heavenly bodies. For himself, though a private 
arrangement between two of his honourable neighbours 
(here he looked hard at the Earth and Venus) had pre- 
vented his hitherto paying that close attention to the pre- 
dictions of the Nautical Almanac which he declared he al- 
ways had wished to do; yet he felt consoled by knowing 
that the conductors of that work had every disposition to 
take his peculiar circumstances into consideration. He de- 
clared that he had never passed the wires of a transit with- 
out deeply feeling his inability to adapt himself to the 
present state of his theory; a feeling which he was afraid 
had sometimes caused a slight tremor in his limb. Before 

* See Sir J. Herschel's Astronomy, p. 369. A. De M. 



302 A BUDGET OF PARADOXES. 

he sat down, he expressed a hope that honourable lumi- 
naries would refrain as much as possible from eclipsing 
each other, or causing mutual peturbations. Indeed, he 
should be very sorry to see any interruption of the harmony 
of the spheres. (Applause.) 

The several articles of the New Nautical Almanac were 
then read over without any comment ; only we observed 
that Saturn shook his ring at every novelty, and Jupiter 
gave his belt a hitch, and winked at the satellites at page 
21 of each month. 

The MOON rose to propose a resolution. No one, he 
said, would be surprised at his bringing this matter forward 
in the way he did, when it was considered in how complete 
and satisfactory a manner his motions were now repre- 
sented. He must own he had trembled when the Lords of 
the Admiralty dissolved the Board of Longitude, but his 
tranquillity was more than reestablished by the adoption 
of the new system. He did not know but that any little 
assistance he could give in Nautical Astronomy was be- 
coming of less and less value every day, owing to the 
improvement of chronometers. But there was one thing, 
of which nothing could deprive him he meant the regu- 
lation of the tides. And, perhaps, when his attention was 
not occupied by more than the latter, he should be able to 
introduce a little more regularity into the phenomena. ( Here 
the honourable luminary gave a sort of modest libration, 
which convulsed the meeting with laughter.) They might 
laugh at his natural infirmity if they pleased, but he could 
assure them it arose only from the necessity he was under, 
when young, of watching the motions of his worthy primary. 
He then moved a resolution highly laudatory of the altera- 
tions which appeared in the New Nautical Almanac. 

The EARTH rose, to second the motion. His honour- 
able satellite had fully expressed his opinions on the sub- 
ject. He joined his honourable friend in the focus in wish- 
ing to pay every attention to the Nautical Almanac, but, 



THE NAUTICAL ALMANACK. 303 

really, when so important an alteration had taken place in 
his magnetic pole 3 (hear) and there might, for aught he 
knew, be a successful attempt to reach his pole of rotation, 
he thought he could not answer for the preservation of the 
precession in its present state. (Here the hon. luminary, 
scratching his side, exclaimed, as he sat down, "More steam- 
boats confound 'em!") 

An honourable satellite (whose name we could not learn) 
proposed that the resolution should be immediately des- 
patched, corrected for refraction, when he was called to 
order by the Focal Body, who reminded him that it was 
contrary to the moving orders of the system to take cog- 
nizance of what passed inside the atmosphere of any planet. 

SATURN and PALLAS rose together. (Cries of "New 
member!" and the former gave way.) The latter, in a 
long and eloquent speech, praised the liberality with which 
he and his colleagues had at length been relieved from 
astronomical disqualifications. He thought that it was 
contrary to the spirit of the laws of gravitation to exclude 
any planet from office on account of the eccentricity or in- 
clination of his orbit. Honourable luminaries need not talk 
of the want of convergency of his series. What had they 
to do with any private arrangements between him and the 
general equations of the system? (Murmurs from the 
opposition.) So long as he obeyed the laws of motion, to 
which he had that day taken a solemn oath, he would ask, 
were old planets, which were now so well known that 
nobody trusted them, to. ... 

The FOCAL BODY said he was sorry to break the continu- 
ity of the proceedings, but he thought that remarks upon 
character, with a negative sign, would introduce differ- 

3 Captain Ross had just stuck a bit of brass there. A. De M. 

Sir James Clark Ross (1800-1862) was a rear admiral in the 
British navy and an arctic and antarctic explorer of prominence. 
De Morgan's reference is to Ross's discovery of the magnetic pole 
on June i, 1831. In 1838 he was employed by the Admiralty on a 
magnetic survey of the United Kingdom. He was awarded the 
gold medal of the geographical societies of London and Paris in 1842. 



304 A BUDGET OF PARADOXES. 

ences of too high an order. The honourable luminary must 
eliminate the expression which he had brought out, in 
finite terms, and use smaller inequalities in future. (Hear, 
hear.) 

PALLAS explained, that he was far from meaning to 
reflect upon the orbital character of any planet present. 
He only meant to protest against being judged by any laws 
but those of gravitation, and the differential calculus: he 
thought it most unjust that astronomers should prevent the 
small planets from being observed, and then reproach them 
with the imperfections of the tables, which were the result 
of their own narrow-minded policy. (Cheers.) 

SATURN thought that, as an old planet, he had not been 
treated with due respect. (Hear, from his satellites.) He 
had long foretold the wreck of the system from the friends 
of innovation. Why, he might ask, were his satellites to 
be excluded, when small planets, trumpery comets, which 
could not keep their mean distances (cries of oh! oh!), 
double stars, with graphical approximations, and such ob- 
scure riff-raff of the heavens (great uproar) found room 
enough. So help him Arithmetic, nothing could come of 
it, but a stoppage of all revolution. His hon. friend in the 
focus might smile, for he would be a gainer by such an 
event; but as for him (Saturn), he had something to lose, 
and hon. luminaries well knew that, whatever they might 
think under an atmosphere, above it continual revolution 
was the only way of preventing perpetual anarchy. As to 
the hon. luminary who had risen before him, he was not 
surprised at his remarks, for he had invariably observed that 
he and his colleagues allowed themselves too much latitude. 
The stability of the system required that they should be 
brought down, and he, for one, would exert all his powers 
of attraction to accomplish that end. If other bodies would 
cordially unite with him, particularly his noble friend next 
him, than whom no luminary possessed greater weight 

JUPITER rose to order* He conceived his noble friend 



THE NAUTICAL ALMANACK. 305 

had no right to allude to him in that manner, and was much 
surprised at his proposal, considering the matters which 
remained in dispute between them. In the present state 
of affairs, he would take care never to be in conjunction 
with his hon. neighbour one moment longer than he could 
help. (Cries of "Order, order, no long inequalities," during 
which he sat down.) 

SATURN proceeded to say, that he did not know till then 
that a planet with a ring could affront one who had only a 
belt, by proposing mutual co-operation. He would now 
come to the subject under discussion. He should think 
meanly of his hon. colleagues if they consented to bestow 
their approbation upon a mere astronomical production. 
Had they forgotten that they once were considered the 
arbiters of fate, and the prognosticators of man's destiny? 
What had lost them that proud position? Was it not the 
infernal march of intellect, which, after having turned the 
earth topsy-turvy, was now disturbing the very universe? 
For himself (others might do as they pleased), but he 
stuck to the venerable Partridge, 4 and the Stationers' Com- 
pany, and trusted that they would outlive infidels and an- 
archists, whether of Astronomical or Diffusion of Knowl- 
edge Societies. (Cries of oh! oh!) 

MARS said he had been told, for he must confess he had 
not seen the work, that the places of the planets were given 
for Sundays. This, he must be allowed to say, was an in- 
decorum he had not expected ; and he was convinced the 
Lords of the Admiralty had given no orders to that effect. 
He hoped this point would be considered in the measure 
which had been introduced in another place, and that some 

4 John Partridge (1644-1715), the well-known astrologer and 
almanac maker. Although bound to a shoemaker in his early boy- 
hood, he had acquired enough Latin at the age of eighteen to read 
the works of the astrologers. He then mastered Greek and Hebrew 
and studied medicine. In 1680 he began the publication of his al- 
manac, the Merlinus Liberatus, a book that acquired literary celeb- 
rity largely through the witty comments upon it by such writers as 
Swift and Steele. 



306 A BUDGET OF PARADOXES. 

one would move that the prohibition against travelling on 
Sundays extend to the heavenly as well as earthly bodies. 

Several of the stars here declared, that they had been 
much annoyed by being observed on Sunday evenings, 
during the hours of divine service. 

The room was then cleared for a division, but we are 
unable to state what took place. Several comets-at-arms 
were sent for, and we heard rumors of a personal collision 
having taken place between two luminaries in opposition. 
We were afterwards told that the resolution was carried 
by a majority, and the luminaries elongated at 2 h. 15 m. 
33,41 s. sidereal time. 

* * * It is reported, but we hope without foundation, that 
Saturn, and several other discontented planets, have ac- 
cepted an invitation from Sirius to join his system, on the 
most liberal appointments. We believe the report to have 
originated in nothing more than the discovery of the annual 
parallax of Sirius from the orbit of Saturn; but we may 
safely assure our readers that no steps have as yet been 
taken to open any communication. 

We are also happy to state, that there is no truth in the 
rumor of the laws of gravitation being about to be re- 
pealed. We have traced this report, and find it originated 
with a gentleman living near Bath (Captain Forman, R.N), 5 
whose name we forbear to mention. 

A great excitement has been observed among the neb- 
ulae, visible to the earth's southern hemisphere, particularly 
among those which have not yet been discovered from 
thence. We are at a loss to conjecture the cause, but we 
shall not fail to report to our readers the news of any move- 
ment which may take place. (Sir J. Herschel's visit. He 
could just see this before he went out.) 

6 See note i on page 296. 



WOODLEY'S DIVINE SYSTEM. 307 



WOODLEY'S DIVINE SYSTEM. 

A Treatise on the Divine System of the Universe, by Captain 
Woodley, R.N., 1 and as demonstrated by his Universal Time- 
piece, and universal method of determining a ship's longitude 
by the apparent true place of the moon; with an introduction 
refuting the solar system of Copernicus, the Newtonian phi- 
losophy, and mathematics. 1834.2 8vo. 

Description of the Universal Time-piece. (4pp. I2mo.) 

I think this divine system was published several years 
before, and was republished with an introduction in 1834. 3 
Capt. Woodley was very sure that the earth does not move : 
he pointed out to me, in a conversation I had with him, 
something I forget what in the motion of the Great 
Bear, visible to any eye, which could not possibly be if the 
earth moved. He was exceedingly ignorant, as the follow- 
ing quotation from his account of the usual opinion will 
show: 

"The north pole of the Earth's axis deserts, they say, 
the north star or pole of the Heavens, at the rate of 1 in 
71% years. . .The fact is, nothing can be more certain than 
that the Stars have not changed their latitudes or declina- 
tions one degree in the last 71% years." 

This is a strong specimen of a class of men by whom 
all accessible persons who have made any name in science 
are hunted. It is a pity that they cannot be admitted into 
scientific societies, and allowed fairly to state their cases, 
and stand quiet cross-examination, being kept in their an- 
swers very close to the questions, and the answers written 
down. I am perfectly satisfied that if one meeting in the 
year were devoted to the hearing of those who chose to 
come forward on such conditions, much good would be 
done. But I strongly suspect few would come forward 

1 William Woodley also published several almanacs (1838, 1839, 
1840) after his rejection by the Astronomical Society in 1834. 

2 It appeared at London. 

8 The first edition appeared in 1830, also at London. 



308 A BUDGET OF PARADOXES. 

at first, and none in a little while: and I have had some 
experience of the method I recommend, privately tried. 
Capt. Woodley was proposed, a little after 1834, as a Fellow 
of the Astronomical Society; and, not caring whether he 
moved the sun or the earth, or both I could not have 
stood neither I signed the proposal. I always had a sneak- 
ing kindness for paradoxers, such a one, perhaps, as Petit 
Andre had for his lambs, as he called them. There was so 
little feeling against his opinions, that he only failed by a 
fraction of a ball. Had I myself voted, he would have 
been elected ; but being engaged in conversation, and not 
having heard the slightest objection to him, I did not think 
it worth while to cross the room for the purpose. I re- 
gretted this at the time, but had I known how ignorant he 
was I should not have supported him. Probably those who 
voted against him knew more of his book than I did. 

I remember no other instance of exclusion from a scien- 
tific society on the ground of opinion, even if this be one ; 
of which it may be that ignorance had more to do with it 
than paradoxy. Mr. Frend, 4 a strong anti-Newtonian, was 
a Fellow of the Astronomical Society, and for some years 
in the Council. Lieut. Kerigan 5 was elected to the Royal 
Society at a time when his proposers must have known that 
his immediate object was to put F.R.S. on the title-page of 
a work against the tides. To give all I know, I may add 
that the editor of some very ignorant bombast about the 
"forehead of the solar sky," who did not know the differ- 
ence between Bailly* and Baity, 7 received hints which in- 
duced him to withdraw his proposal for election into the 
Astronomical Society. But this was an act of kindness ; 

4 See note i, page 196. 

6 Thomas Kerigan wrote The Young Navigator's Guide to the 
siderial and planetary parts of Nautical Astronomy (London, 1821, 
second edition 1828), a work on eclipses (London, 1844), and the 
work on tides (London, 1847) to which De Morgan refers. 

8 Jean Sylvain Bailly, who was guillotined. See note i, page 166. 
T See note 2, page 309. 



ON JOHN FLAMSTEED. 309 

for if he had seen Mr. Baily in the chair, with his head on, 
he might have been political historian enough to faint away. 

De la formation des Corps. Par Paul Laurent. 8 Nancy, 1834, 
8vo. 

Atoms, and ether, and ovules or eggs, which are planets, 
and their eggs, which are satellites. These speculators can 
create worlds, in which they cannot be refuted ; but none of 
them dare attack the problem of a grain of wheat, and its 
passage from a seed to a plant, bearing scores of seeds like 
what it was itself. 

ON JOHN FLAMSTEED. 

An account of the Rev. John Flamsteed, 1 the First Astronomer- 
Royal. ... By Francis Baily, 2 Esq. London, 1835, 4 to - Supple- 
ment, London, 1837, 4to. 

My friend Francis Baily was a paradoxer: he brought 
forward things counter to universal opinion. That Newton 
was impeccable in every point was the national creed; and 
failings of temper and conduct would have been utterly 
disbelieved, if the paradox had not come supported by very 
unusual evidence. Anybody who impeached Newton on 
existing evidence might as well have been squaring the 
circle, for any attention he would have got. About this 
book I will tell a story. It was published by the Admiralty 
for distribution ; and the distribution was entrusted to Mr. 
Baily. On the eve of its appearance, rumors of its extra- 
ordinary revelations got about, and persons of influence 
applied to the Admiralty for copies. The Lords were in a 
difficulty : but on looking at the list they saw names, as they 

8 Laurent seems to have had faint glimpses of the modern theory 
of matter. He is, however, unknown. 

1 See note 4, page 87. 

2 Francis Baily (1774-1844) was a London stockbroker. His 
interest in science in general and in astronomy in particular led to 
his membership in the Royal Society and to his presidency of the 
Astronomical Society. He wrote on interest and annuities (1808), 
but his chief works were on astronomy. 



310 A BUDGET OF PARADOXES. 

thought, which were so obscure that they had a right to 
assume Mr. Baily had included persons who had no claim 
to such a compliment as presentation from the Admiralty. 
The Secretary requested Mr. Baily to call upon him. "Mr. 
Baily, my Lords are inclined to think that some of the per- 
sons in this list are perhaps not of that note which would 
justify their Lordships in presenting this work." "To whom 
does your observation apply, Mr. Secretary ?" "Well, now, 
let us examine the list; let me see; now, now, now, 
come! here's Gauss 3 who's Gauss'?" "Gauss, Mr. Sec- 
retary, is the oldest mathematician now living, and is gen- 
erally thought to be the greatest." "O-o-oh ! Well, Mr. 
Baily, we will see about it, and I will write you a letter." 
The letter expressed their Lordships' perfect satisfaction 
with the list. 

There was a controversy about the revelations made in 
this work ; but as the eccentric anomalies took no part in it, 
there is nothing for my purpose. The following valentine 
from Mrs. Flamsteed. 4 which I found among Baily's papers, 
illustrates some of the points: 

"3 Astronomers' Row, Paradise : February 14, 1836. 

"Dear Sir, I suppose you hardly expected to receive a 
letter from me, dated from this place; but the truth is, a 
gentleman from our street was appointed guardian angel to 
the American Treaty, in which there is some astronomical 
question about boundaries. He has got leave to go back to 
fetch some instruments which he left behind, and I take this 
opportunity of making your acquaintance. That America 
has become a wonderful place since I was down among 
you; you have no idea how grand the fire at New York 

'If the story is correctly told Baily must have enjoyed his 
statement that Gauss was "the oldest mathematician now living." 
As a matter of fact he was then only 58, three years the junior of 
Baily himself. Gauss was born in 1777 and died in 1855, and Baily 
was quite right in saying that he was "generally thought to be the 
greatest" mathematician then living. 

'Margaret Cooke, who married Flamsteed in 1692. 



ON JOHN FLAMSTEED. 311 

looked up here. Poor dear Mr. Flamsteed does not know 
I am writing a letter to a gentleman on Valentine's day ; he 
is walked out with Sir Isaac Newton (they are pretty good 
friends now, though they do squabble a little sometimes) 
and Sir William Herschel, to see a new nebula. Sir Isaac 
says he can't make out at all how it is managed ; and I am 
sure I cannot help him. I never bothered my head about 
those things down below, and I don't intend to begin here. 
"I have just received the news of your having written 
a book about my poor dear man. It's a chance that I heard 
it at all ; for the truth is, the scientific gentlemen are some- 
how or other become so wicked, and go so little to church, 
that very few of them are considered fit company for this 
place. If it had not been for Dr. Brinkley, 5 who came here 
of course, I should not have heard about it. He seems a 
nice man, but is not yet used to our ways. As to Mr. Hal- 
ley, 6 he is of course not here; which is lucky for him, for 
Mr. Flamsteed swore the moment he caught him in a place 
where there are no magistrates, he would make a sacrifice 
of him to heavenly truth. It was very generous in Mr. F. 
not appearing against Sir Isaac when he came up, for I am 
told that if he had, Sir Isaac would not have been allowed 
to come in at all. I should have been sorry for that, for he 
is a companionable man enough, only holds his head rather 
higher than he should do. I met him the other day walking 
with Mr. Whiston, 7 and disputing about the deluge. 'Well, 
Mrs. Flamsteed/ says he, 'does old Poke-the-Stars under- 
stand gravitation yet?' Now you must know that is rather 
a sore point with poor dear Mr. Flamsteed. He says that 
Sir Isaac is as crochetty about the moon as ever ; and as to 

E John Brinkley (1763-1835), senior wrangler, first Smith's prize- 
man (1788), Andrews professor of astronomy at Dublin, first As- 
tronomer Royal for Ireland (1792), F.R.S. (1803), Copley medallist, 
president of the Royal Society and Bishop of Cloyne. His Elements 
of Astronomy appeared in 1808. 

" See note 7, page 124. 
7 See note 3, page 133. 



312 A BUDGET OF PARADOXES. 

what some people say about what has been done since his 
time, he says he should like to see somebody who knows 
something about it of himself. For it is very singular that 
none of the people who have carried on Sir Isaac's notions 
have been allowed to come here. 

"I hope you have not forgotten to tell how badly Sir 
Isaac used Mr. Flamsteed about that book. I have never 
quite forgiven him; as for Mr. Flamsteed, he says that as 
long as he does not come for observations, he does not care 
about it, and that he will never trust him with any papers 
again as long as he lives. I shall never forget what a rage 
he came home in when Sir Isaac had called him a puppy. 
He struck the stairs all the way up with his crutch, and said 
puppy at every step, and all the evening, as soon as ever 
a star appeared in the telescope, he called it puppy. I could 
not think what was the matter, and when I asked, he only 
called me puppy. 

"I shall be very glad to see you if you come our way. 
Pray keep up some appearances, and go to church a little. 
St. Peter is always uncommonly civil to astronomers, and in- 
deed to all scientific persons, and never bothers them with 
many questions. If they can make anything out of the case, 
he is sure to let them in. Indeed, he says, it is perfectly 
out of the question expecting a mathematician to be as re- 
ligious as an apostle, but that it is as much as his place is 
worth to let in the greater number of those who come. So 
try if you cannot manage it, for I am very curious to know 
whether you found all the letters. I remain, dear sir, your 
faithful servant, 

"MARGARET FLAMSTEED. 

Francis Baily, Esq. 

"P.S. Mr. Flamsteed has come in, and says he left Sir 
Isaac riding cockhorse upon the nebula, and poring over it 
as if it were a book. He has brought in his old acquaint- 
ance Ozanam, 8 who says that it was always his maxim on 

8 See note 7, page 161. 



ON STEVIN. 313 

earth, that 'il appartient aux docteurs de Sorbonne de dis- 
puter, au Pape de prononcer, et au mathematicien d'aller en 
Paradis en ligne perpendiculaire.' " 9 

ON STEVIN. 

The Secretary of the Admiralty was completely extin- 
guished. I can recall but two instances of demolition as 
complete, though no doubt there are many others. The first 
is in 

Simon Stevin 1 and M. Dumortier. Nieuport, 1845, I2mo. 

M. Dumortier was a member of the Academy of Brus- 
sels : there was a discussion, I believe, about a national 
Pantheon for Belgium. The name of Stevinus suggested 
itself as naturally as that of Newton to an Englishman; 
probably no Belgian is better known to foreigners as illus- 
trious in science. Stevinus is great in the Mecanique Ana- 
lytique of Lagrange f Stevinus is great in the Tristram 
Shandy of Sterne. M. Dumortier, who believed that not 
one Belgian in a thousand knew Stevinus, and who confesses 
with ironical shame that he was not the odd man, protested 
against placing the statue of an obscure man in the Pan- 
theon, to give foreigners the notion that Belgium could 
show nothing greater. The work above named is a slash- 
ing retort: any one who knows the history of science ever 
so little may imagine what a dressing was given, by mere 
extract from foreign writers. The tract is a letter signed 
J. du Fan, but this is a pseudonym of Mr. Van de Weyer. 3 
The Academician says Stevinus was a man who was not 

"Tt becomes the doctors of the Sorbonne to dispute, the Pope 
to decree, and the mathematician to go to Paradise on a perpen- 
dicular line." 

1 See note 10, page 83. 
8 See note 3, page 288. 

s Sylvain van de Weyer, who was born at Louvain in 1802. He 
was a jurist and statesman, holding the portfolio for foreign affairs 
(1831-1833), and being at one time ambassador to England. 



314 A BUDGET OF PARADOXES. 

without merit for the time at which he lived: Sir! is the 
answer, he was as much before his own time as you are 
behind yours. How came a man who had never heard of 
Stevinus to be a member of the Brussels Academy ? 

The second story was told me by Mr. Crabb Robinson, 4 
who was long connected with the Times, and intimately ac- 
quainted with Mr. W***. 5 When W*** was an under- 
graduate at Cambridge, taking a walk, he came to a stile, 
on which sat a bumpkin who did not make way for him: 
the gown in that day looked down on the town. "Why do 
you not make way for a gentleman?" "Eh?" "Yes, why 
do you not move? You deserve a good hiding, and you 
shall get it if you don't take care!" The bumpkin raised 
his muscular figure on its feet, patted his menacer on the 
head, and said, very quietly, "Young man! I'm Cribb." 6 
W*** seized the great pugilist's hand, and shook it warmly, 
got him to his own rooms in college, collected some friends, 
and had a symposium which lasted until the large end of 
the small hours. 

FINLEYSON AS A PARADOXER. 

God's Creation of the Universe as it is, in support of the Scrip- 
tures. By Mr. Finleyson. 1 Sixth Edition, 1835, 8vo. 

4 Henry Crabb Robinson (1775-1867), correspondent of the 
Times at Altona and in the Peninsula, and later foreign editor. 
He was one of the founders of the Athenaeum Club and of University 
College, London. He seems to have known pretty much every one 
of his day, and his posthumous Diary attracted attention when it 
appeared. 

5 Was this Whewell, who was at Trinity from 1812 to 1816 and 
became a fellow in 1817? 

8 Tom Cribb (1781-1848) the champion pugilist. He had worked 
as a coal porter and hence received his nickname, the Black Dia- 
mond. 

1 John Finleyson, or Finlayson, was born in Scotland in 1770 
and died in London in 1854. He published a number of pamphlets 
that made a pretense to being scientific. Among his striking phrases 
and sentences are the statements that the stars were made "to amuse 
us in observing them"; that the earth is "not shaped like a garden 
turnip as the Newtonians make it," and that the stars are "oval- 
shaped immense masses of frozen water." The first edition of the 
work here mentioned appeared at London in 1830. 



FINLEYSON AS A PARADOXER. 315 

This writer, by his own account, succeeded in delivering 
the famous Lieut. Richard Brothers 2 from the lunatic 
asylum, and tending him, not as a keeper but as a disciple, 
till he died. Brothers was, by his own account, the nephew 
of the Almighty, and Finleyson ought to have been the 
nephew of Brothers. For Napoleon came to him in a 
vision, with a broken sword and an arrow in his side, be- 
seeching help: Finleyson pulled out the arrow, but refused 
to give a new sword; whereby poor Napoleon, though he 
got off with life, lost the battle of Waterloo. This story 
was written to the Duke of Wellington, ending with "I 
pulled out the arrow, but left the broken sword. Your 
Grace can supply the rest, and what followed is amply re- 
corded in history." The book contains a long account of 
applications to Government to do three things: to pay 
2,000/. for care taken of Brothers, to pay 10,000/. for dis- 
covery of the longitude, and to prohibit the teaching of 
the Newtonian system, which makes God a liar. The suc- 
cessive administrations were threatened that they would 
have to turn out if they refused, which, it is remarked, 
came to pass in every case. I have heard of a joke of Lord 
Macaulay, that the House of Commons must be the Beast 
of the Revelations, since 658 members, with the officers 
necessary for the action of the House, make 666. Macaulay 
read most things, and the greater part of the rest: so that 
he might be suspected of having appropriated as a joke 
one of Finleyson's serious points "I wrote Earl Grey 3 
upon the 13th of July, 1831, informing him that his Reform 

2 Richard Brothers (1757-1824) was a native of Newfoundland. 
He went to London when he was about 30, and a little later set forth 
his claim to being a descendant of David, prince of the Hebrews, 
and ruler of the world. He was confined as a criminal lunatic in 
1795 but was released in 1806. 

3 Charles Grey (1764-1845), second Earl Grey, Viscount Howick, 
was then Prime Minister. The Reform Bill was introduced and de- 
feated in 1831. The following year, with the Royal guarantees to 
allow him to create peers, he finally carried the bill in spite of "the 
number of the beast." 



316 A BUDGET OF PARADOXES. 

Bill could not be carried, as it reduced the members below 
the present amount of 658, which, with the eight principal 
clerks or officers of the House, make the number 666." 
But a witness has informed me that Macaulay's joke was 
made in his hearing a great many years before the Reform 
Bill was proposed ; in fact, when both were students at 
Cambridge. Earl Grey was, according to Finleyson, a des- 
cendant of Uriah the Hittite. For a specimen of Lieut. 
Brothers, this book would be worth picking up. Perhaps 
a specimen of the Lieutenant's poetry may be acceptable: 
Brothers loquitur, remember: 

"Jerusalem ! Jerusalem ! shall be built again ! 

More rich, more grand then ever; 
And through it shall Jordan flow!(!) 

My people's favourite river. 
There I'll erect a splendid throne, 

And build on the wasted place; 
To fulfil my ancient covenant 

To King David and his race. 
******** 

"Euphrates' stream shall flow with ships, 

And also my wedded Nile; 
And on my coast shall cities rise, 

Each one distant but a mile. 
******* 

"My friends the Russians on the north 

With Persees and Arabs round, 
Do show the limits of my land, 

Here! Here! then I mark the ground." 

ON THEOLOGICAL PARADOXERS. 

Among the paradoxers are some of the theologians who 
in their own organs of the press venture to criticise science. 
These may hold their ground when they confine themselves 
to the geology of long past periods and to general cosmog- 
ony : for it is the tug of Greek against Greek ; and both sides 
deal much in what is grand when called hypothesis, petty 
when called supposition. And very often they are not con- 
spicuous when they venture upon things within knowledge ; 



ON THEOLOGICAL PARADOXERS. 



317 



wrong, but not quite wrong enough for a Budget of Para- 
doxes. One case, however, is destined to live, as an in- 
stance of a school which finds writers, editors, and readers. 
The double stars have been seen from the seventeenth cen- 
tury, and diligently observed by many from the time of Wm. 
Herschel, who first devoted continuous attention to them. 
The year 1836 was that of a remarkable triumph of astro- 
nomical prediction. The theory of gravitation had been 
applied to the motion of binary stars about each other, in 
elliptic orbits, and in that year the two stars of y Virginis, 
as had been predicted should happen within a few years of 
that time for years are small quantities in such long revo- 
lutions the two stars came to their nearest: in fact, they 
appeared to be one as much with the telescope as without it. 
This remarkable turning-point of the history of a long and 
widely-known branch of astronomy was followed by an 
article in the Church of England Quarterly Review for 
April 1837, written against the Useful Knowledge Society. 
The notion that there are any such things as double stars 
is (p. 460) implied to be imposture or delusion, as in the 
following extract. I suspect that I myself am the Sidrophel, 
and that my companion to the maps of the stars, written for 
the Society and published in 1836, is the work to which the 
writer refers: 

"We have forgotten the name of that Sidrophel who 
lately discovered that the fixed stars were not single stars, 
but appear in the heavens like soles at Billingsgate, in pairs ; 
while a second astronomer, under the influence of that com- 
petition in trade which the political economists tell us is 
so advantageous to the public, professes to show us, through 
his superior telescope, that the apparently single stars are 
really three. Before such wondrous mandarins of science, 
how continually must homunculi like ourselves keep in the 
background, lest we come between the wind and their 
nobility." 

If the homunculus who wrote this be still above ground, 



318 A BUDGET OF PARADOXES. 

how devoutly must he hope he may be able to keep in the 
background ! But the chief blame falls on the editor. The 
title of the article is: 

''The new school of superficial pantology; a speech in- 
tended to be delivered before a defunct Mechanics' Insti- 
tute. By Swallow Swift, late M.P. for the Borough of 
Cockney-Cloud, Witsbury : reprinted Balloon Island, Bubble 
year, month Ventose. Long live Charlatan!" 

As a rule, orthodox theologians should avoid humor, a 
weapon which all history shows to be very difficult to employ 
in favor of establishment, and which, nine times out of ten, 
leaves its wielder fighting on the side of heterodoxy. Theo- 
logical argument, when not enlivened by bigotry, is seldom 
worse than narcotic: but theological fun, when not covert 
heresy, is almost always sialagogue. The article in question 
is a craze, which no editor should have admitted, except after 
severe inspection by qualified persons. The author of this 
wit committed a mistake which occurs now and then in old 
satire, the confusion between himself and the party aimed 
at. He ought to be reviewing this fictitious book, but every 
now and then the article becomes the book itself; not by 
quotation, but by the writer forgetting that he is not Mr. 
Swallow Swift, but his reviewer. In fact he and Mr. S. 
Swift had each had a dose of the Devil's Elixir. A novel 
so called, published about forty years ago, proceeds upon 
a legend of this kind. If two parties both drink of the 
elixir, their identities get curiously intermingled ; each turns 
up in the character of the other throughout the three vol- 
umes, without having his ideas clear as to whether he be 
himself or the other. There is a similar confusion in the 
answer made to the famous E pistole? Obscurorum Viro- 
it is headed Lamentationes Obscurorum Virorum. 2 



1 The letters of obscure men, the Epistola obscurorum virorum 
ad venerabilem virum Magistrum Ortuinum Gratium Dauentriensem, 
by Joannes Crotus, Ulrich von Hutten, and others appeared at 
Venice about 1516. 

2 The lamentations of obscure men, the Lamentationes obscuro- 



ON THEOLOGICAL PARADOXERS. 319 

This is not a retort of the writer, throwing back the impu- 
tation: the obscure men who had been satirized are them- 
selves made, by name, to wince under the disapprobation 
which the Pope had expressed at the satire upon themselves. 

Of course the book here reviewed is a transparent for- 
gery. But I do not know how often it may have happened 
that the book, in the journals which always put a title at the 
head, may have been written after the review. About the 
year 1830 a friend showed me the proof of an article of his 
on the malt tax, for the next number of the Edinburgh 
Review. Nothing was wanting except the title of the book 
reviewed; I asked what it was. He sat down, and wrote 
as follows at the head, "The Maltster's Guide (pp. 124)," 
and said that would do as well as anything. 

But I myself, it will be remarked, have employed such 
humor as I can command "in favor of establishment." 
What it is worth I am not to judge ; as usual in such cases, 
those who are of my cabal pronounce it good, but cyclom- 
eters and other paradoxers either call it very poor, or com- 
mend it as sheer buffoonery. Be it one or the other, I ob- 
serve that all the effective ridicule is, in this subject, on 
the side of establishment. This is partly due to the diffi- 
culty of quizzing plain and sober demonstration ; but so 
much, if not more, to the ignorance of the paradoxers. 
For that which cannot be ridiculed, can be turned into ridi- 
cule by those who know how. But by the time a person 
is deep enough in negative quantities, and impossible quan- 
tities, to be able to satirize them, he is caught, and being 
inclined to become a user, shrinks from being an abuser. 
Imagine a person with a gift of ridicule, and knowledge 
enough, trying his hand on the junction of the assertions 
which he will find in various books of algebra. First, that 
a negative quantity has no logarithm ; secondly, that a neg- 

rum virorum, non prohibcte per sedem Apostolicam. Epistola D. 
Erasmi Roterodami -.quid de obscuris sentiat, by G. Ortwinus, ap- 
peared at Cologne in. 1518: 



320 A BUDGET OF PARADOXES. 

ative quantity has no square root ; thirdly, that the first 
non-existent is to the second as the circumference of a 
circle to its diameter. One great reason of the allowance 
of such unsound modes of expression is the confidence felt 
by the writers that V ~~ 1 anc ^ ^S (~~ 1) w ^ niake their way, 
however inaccurately described. I heartily wish that the 
cyclometers had knowledge enough to attack the weak 
points of algebraical diction : they would soon work a bene- 
ficial change. 3 

AN EARLY METEOROLOGIST. 

Recueil de ma vie, mes ouvrages et mes pensees. Par Thomas 
Ignace Marie Forster. 1 Brussels, 1836, I2mo. 

Mr. Forster, an Englishman settled at Bruges, was an 
observer in many subjects, but especially in meteorology. 
He communicated to the Astronomical Society, in 1848, the 
information that, in the registers kept by his grandfather, 
his father, and himself, beginning in 1767, new moon on 
Saturday was followed, nineteen times out of twenty, by 
twenty days of rain and wind. This statement being pub- 
lished in the Athen&um, a cluster of correspondents averred 
that the belief is common among seamen, in all parts of the 
world, and among landsmen too. Some one quoted a dis- 
tich: 

"Saturday's moon and Sunday's full 
Never were fine and never wull." 

8 The criticism was timely when De Morgan wrote it. At present 
it would have but little force with respect to the better class of 
algebras. 

1 Thomas Ignatius Maria Forster (1789-1860) was more of a 
man than one would infer from this satire upon his theory. He 
was a naturalist, astronomer, and physiologist. In 1812 he published 
his Researches about Atmospheric Phenomena, and seven years later 
(July 3, 1819) he discovered a comet. With Sir Richard Phillips 
he founded a Meteorological Society, but it was short lived. He 
declined a fellowship in the Royal Society because he disapproved 
of certain of its rules, so that he had a recognized standing in his 
day. The work mentioned by De Morgan is the second edition, 
the first having appeared at Frankfort on the Main in 1835 under 
the title, Recueil des ouvrages et des pensees d'un physicien et 
metaphysicien. 



AN EARLY METEOROLOGIST. 321 

Another brought forward: 

"If a Saturday's moon 
Comes once in seven years it comes too soon." 

Mr. Forster did not say he was aware of the proverbial 
character of the phenomenon. He was a very eccentric 
man. He treated his dogs as friends, and buried them with 
ceremony. He quarrelled with the cure of his parish, who 
remarked that he could not take his dogs to heaven with 
him. I will go nowhere, said he, where I cannot take my 
dog. He was a sincere Catholic : but there is a point beyond 
which even churches have no influence. 

The following is some account of the announcement of 
1849. The Athenaum (Feb. 17), giving an account of the 
meeting of the Astronomical Society in December, 1858, 
says: 

"Dr. Forster of Bruges, who is well known as a meteor- 
ologist, made a communication at which our readers will 
stare : he declares that by journals of the weather kept by his 
grandfather, father, and himself, ever since 1767, to the 
present time, whenever the new moon has fallen on a Satur- 
day, the following twenty days have been wet and windy, in 
nineteen cases out of twenty. In spite of our friend Zadkiel 2 
and the others who declare that we would smother every 
truth that does not happen to agree with us, we are glad 
to see that the Society had the sense to publish this com- 
munication, coming, as it does, from a veteran observer, 
and one whose love of truth is undoubted. It must be 
that the fact is so set down in the journals, because Dr. 
Forster says it: and whether it be only a fact of the jour- 
nals, or one of the heavens, can soon be tried. The new 
moon of March next, falls on Saturday the 24th, at 2 in the 
afternoon. We shall certainly look out." 

2 Zadkiel, whose real name was Richard James Morrison (1795- 
1874), was in his early years an officer in the navy. In 1831 he 
began the publication of the Herald of Astrology, which was con- 
tinued as Zadkiel 9 s Almanac. His name became familiar through- 
out Great Britain as a result. 



322 A BUDGET OF PARADOXES. 

The following appeared in the number of March 31 : 
"The first Saturday Moon since Dr. Forster's announce- 
ment came off a week ago. We had previously received 
a number of letters from different correspondents all to 
the effect that the notion of new moon on Saturday bringing 
wet weather is one of widely extended currency. One cor- 
respondent (who gives his name) states that he has con- 
stantly heard it at sea, and among the farmers and peas- 
antry in Scotland, Ireland, and the North of England. He 
proceeds thus: 'Since 1826, nineteen years of the time I 
have spent in a seafaring life. I have constantly observed, 
though unable to account for, the phenomenon. I have also 
heard the stormy qualities of a Saturday's moon remarked 
by American, French, and Spanish seamen; and, still more 
distant, a Chinese pilot, who was once doing duty on board 
my vessel seemed to be perfectly cognizant of the fact.' 
So that it seems we have, in giving currency to what we 
only knew as a very curious communication from an earnest 
meteorologist, been repeating what is common enough 
among sailors and farmers. Another correspondent affirms 
that the thing is most devoutly believed in by seamen ; who 
would as soon sail on a Friday as be in the Channel after 
a Saturday moon. After a tolerable course of dry weather, 
there was some snow, accompanied by wind on Saturday 
last, here in London ; there were also heavy louring clouds. 
Sunday was cloudy and cold, with a little rain ; Monday 
was louring, Tuesday unsettled ; Wednesday quite over- 
clouded, with rain in the morning. The present occasion 
shows only a general change of weather with a tendency 
towards rain. If Dr. Forster's theory be true, it is decidedly 
one of the minor instances, as far as London weather is con- 
cerned. It will take a good deal of evidence to make us 
believe in the omen of a Saturday Moon. But, as we have 
said of the Poughkeepsie Seer, the thing is very curious 
whether true or false. Whence comes this universal proverb 
and a hundred others while the meteorological observer 



AN EARLY METEOROLOGIST. 323 

cannot, when he puts down a long series of results, detect 
any weather cycles at all ? One of our correspondents wrote 
us something of a lecture for encouraging, he said, the 
notion that names could influence the weather. He mis- 
takes the question. If there be any weather cycles depend- 
ing on the moon, it is possible that one of them may be so 
related to the week cycle of seven days, as to show recur- 
rences which are of the kind stated, or any other. For ex- 
ample, we know that if the new moon of March fall on a 
Saturday in this year, it will most probably fall on a Satur- 
day nineteen years hence. This is not connected with the 
spelling of Saturday but with the connection between the 
motions of the sun and moon. Nothing but the Moon can 
settle the question and we are willing to wait on her for 
further information. If the adage be true, then the phi- 
losopher has missed what lies before his eyes ; if false, then 
the world can be led by the nose in spite of the eyes. Both 
these things happen sometimes ; and we are willing to take 
whichever of the two solutions is borne out by future facts. 
In the mean time, we announce the next Saturday Moon 
for the 18th of August." 

How many coincidences are required to establish a law 
of connection? It depends on the way in which the mind 
views the matter in question. Many of the paradoxers are 
quite set up by a very few instances. I will now tell a story 
about myself, and then ask them a question. 

So far as instances can prove a law, the following is 
proved : no failure has occurred. Let a clergyman be known 
to me, whether by personal acquaintance or correspondence, 
or by being frequently brought before me by those with 
whom I am connected in private life: that clergyman does 
not, except in few cases, become a bishop ; but if he become 
a bishop, he is sure, first or last, to become an arch-bishop. 
This has happened in every case. As follows: 

1. My last schoolmaster, a former Fellow of Oriel, was 



324 A BUDGET OF PARADOXES. 

a very intimate college friend of Richard Whately, 3 a 
younger man. Struck by his friend's talents, he used to 
talk of him perpetually, and predict his future eminence. 
Before I was sixteen, and before Whately had even given his 
Bampton Lectures, I was very familiar with his name, and 
some of his sayings. I need not say that he became Arch- 
bishop of Dublin. 

2. When I was a child, a first cousin of John Bird Sum- 
ner* married a sister of my mother. I cannot remember the 
time when I first heard his name, but it was made very 
familiar to me. In time he became Bishop of Chester, and 
then, Archbishop of Canterbury. My reader may say that 
Dr. C. R. Sumner, 5 Bishop of Winchester, has just as good a 
claim: but it is not so: those connected with me had more 
knowledge of Dr. J. B. Sumner ; and said nothing, or next 
to nothing, of the other. Rumor says that the Bishop of 
Winchester has declined an Archbishopric : if so, my rule is 
a rule of gradations. 

3. Thomas Musgrave, 7 Fellow of Trinity College, Cam- 
bridge, was Dean of the college when I was an under- 
graduate: this brought me into connection with him, he 
giving impositions for not going to chapel, I writing them 
out according. We had also friendly intercourse in after 
life ; I forgiving, he probably forgetting. Honest Tom Mus- 

8 See note 1, page 246. 

* Sumner (1780-1862) was an Eton boy. He went to King's 
College, Cambridge, and was elected fellow in 1801. He took many 
honors, and in 1807 became M.A. He was successively Canon of 
Durham (1820), Bishop of Chester (1828), and Archbishop of 
Canterbury (1848). Although he voted for the Catholic Relief Bill 
(1829) and the Reform Bill (1832), he opposed the removal of 
Jewish disabilities. 

"Charles Richard Sumner (1790-1874) was not only Bishop of 
Winchester (1827), but also Bishop of Llandaff and Dean of St. 
Paul's, London (1826). He lost the king's favor by voting for the 
Catholic Relief Bill. 

6 John Bird Sumner, brother of Charles Richard. 

'Thomas Musgrave (1788-1860) became Fellow of Trinity in 
1812, and senior proctor in 1831. He was also Dean of Bristol. 



AN EARLY METEOROLOGIST. 325 

grave, as he used to be called, became Bishop of Hereford, 
and Archbishop of York. 

4. About the time when I went to Cambridge, I heard 
a great deal about Mr. C. T. Longley, 8 of* Christchurch, 
from a cousin of my own of the same college, long since 
deceased, who spoke of him much, and most affectionately. 
Dr. Longley passed from Durham to York, and thence to 
Canterbury. I cannot quite make out the two Archbishop- 
rics ; I do not remember any other private channel through 
which the name came to me: perhaps Dr. Longley, having 
two strings to his bow, would have been one archbishop if 
I had never heard of him. 

5. When Dr. Wm. Thomson 9 was appointed to the see 
of Gloucester in 1861, he and I had been correspondents 
on the subject of logic on which we had both written for 
about fourteen years. On his elevation I wrote to him, 
giving the preceding instances, and informing him that he 
would certainly be an Archbishop. The case was a strong 
one, and the law acted rapidly ; for Dr. Thomson's elevation 
to the see of York took place in 1862. 

Here are five cases; and there is no opposing instance. 
I have searched the almanacs since 1828, and can find no 
instance of a Bishop not finally Archbishop of whom I had 
known through private sources, direct or indirect. Now 
what do my paradoxers say? Is this a pre-established har- 
mony, or a chain of coincidences? And how many in- 
stances will it require to establish a law? 10 

"Charles Thomas Longley (1794-1868) was educated at West- 
minster School and at Christ Church, Oxford. He became M.A. in 
1818 and D.D. in 1829. Besides the bishoprics mentioned he was 
Bishop of Ripon (1836-1856), and before that was headmaster of 
Harrow (1829-1836). 

"Thomson (1819-1890) was scholar and fellow of Queen's Col- 
lege, Oxford. He became chaplain to the Queen in 1859. 

10 This is worthy of the statistical psychologists of the present 
day. 



326 A BUDGET OF PARADOXES. 



THE HERSCHEL HOAX. 

Some account of the great astronomical discoveries lately made 
by Sir John Herschel at the Cape of Good Hope. Second 
Edition. London, I2mo. 1836. 

This is a curious hoax, evidently written by a person 
versed in astronomy and clever at introducing probable 
circumstances and undesigned coincidences. 1 It first ap- 
peared in a newspaper. It makes Sir J. Herschel discover 
men, animals, etc. in the moon, of which much detail is 
given. There seems to have been a French edition, the 
original, and English editions in America, whence the 
work came into Britain: but whether the French was pub- 
lished in America or at Paris I do not know. There is no 
doubt that it was produced in the United States, by M. 
Nicollet, 2 an astronomer, once of Paris, and a fugitive of 
some kind. About him I have heard two stories. First 
that he fled to America with funds not his own, and that this 
book was a mere device to raise the wind. Secondly, that 
he was a protege of Laplace, and of the Polignac party, 
and also an outspoken man. That after the revolution he 
was so obnoxious to the republican party that he judged it 
prudent to quit France; which he did in debt, leaving 
money for his creditors, but not enough, with M. Bouvard. 
In America he connected himself with an assurance office. 

1 The famous Moon Hoax was written by Richard Adams Locke, 
who was born in New York in 1800 and died in Staten Island in 
1871. He was at one time editor of the Sun, and the Hoax appeared 
in that journal in 1835. It was reprinted in London (1836) and 
Germany, and was accepted seriously by most readers. It was pub- 
lished in book form in New York in 1852 under the. title The Moon 
Hoax. Locke also wrote another hoax, the Lost Manuscript of 
Mungo Park, but it attracted relatively little attention. 

*It is true that Jean-Nicolas Nicollet (1756-1843) was at that 
time in the United States, but there does not seem to be any very 
tangible evidence to connect him with the story. He was secretary 
and librarian of the Paris observatory (1817), member of the 
Bureau of Longitudes (1822), and teacher of mathematics in the 
Lycee Louis-le-Grand. Having lost his money through speculations 
he left France for the United States in 1831 and became connected 
with the government survey of the Mississippi Valley. 



SOME MORE METEOROLOGY. 327 

The moon-story was written, and sent to France, chiefly 
with the intention of entrapping M. Arago, Nicollet's es- 
pecial foe, into the belief of it. And those who narrate 
this version of the story wind up by saying that M. Arago 
was entrapped, and circulated the wonders through Paris, 
until a letter from Nicollet to M. Bouvard 3 explained the 
hoax. I have no personal knowledge of either story: but 
as the poor man had to endure the first, it is but right that 
the second should be told with it. 

SOME MORE METEOROLOGY. 

The Weather Almanac for the Year 1838. By P. Murphy, 1 Esq., 
M.N.S. 

By M. N. S. is meant member of no society. This al- 
manac bears on the title-page two recommendations. The 
Morning Post calls it one of the most important-if-true 
publications of our generation. The Times says: "If the 
basis of his theory prove sound, and its principles be sanc- 
tioned by a more extended experience, it is not too much to 
say that the importance of the discovery is equal to that 
of the longitude." Cautious journalist! Three times that 
of the longitude would have been too little to say. That the 
landsman might predict the weather of all the year, at its 
beginning, Jack would cheerfully give up astronomical 
longitude the problem altogether, and fall back on chro- 
nometers with the older Ls, lead, latitude, and look-out, 
applied to dead-reckoning. Mr. Murphy attempted to give 
the weather day by day : thus the first seven days of March 

= This was Alexis Bouvard (1767-1843), who made most of the 
computations for Laplace's Mecanique celeste (1793). He discovered 
eight new comets and calculated their orbits. In his tables of 
Uranus (1821) he attributed certain perturbations to the presence 
of an undiscovered planet, but unlike Leverrier and Adams he did 
not follow up this clue and thus discover Neptune. 

1 Patrick Murphy (1782-1847) awoke to find himself famous 
because of his natural guess that there would be very cold weather 
on January 20, although that is generally the season of lowest tem- 
perature. It turned out that his forecasts were partly right on 168 
days and very wrong on 197 days. 



328 A BUDGET OF PARADOXES. 

bore Changeable ; Rain ; Rain ; Rain - win d ; Changeable ; 
Fair; Changeable. To aim at such precision as to put a 
fair day between two changeable ones by weather theory 
was going very near the wind and weather too. Murphy 
opened the year with cold and frost ; and the weather did the 
same. But Murphy, opposite to Saturday, January 20, put 
down "Fair, Probable lowest degree of winter temperature." 
When this Saturday came, it was not merely the probably 
coldest of 1838, but certainly the coldest of many consecu- 
tive years. Without knowing anything of Murphy, I felt 
it prudent to cover my nose with my glove as I walked the 
street at eight in the morning. The fortune of the Almanac 
was made. Nobody waited to see whether the future would 
dement the prophecy : the shop was beset in a manner which 
brought the police to keep order ; and it was said that the 
Almanac for 1838 was a gain of 5,000/. to the owners. It 
very soon appeared that this was only a lucky hit: the 
weather-prophet had a modified reputation for a few years ; 
and is now no more heard of. A work of his will presently 
appear in the list. 

THE GREAT PYRAMIDS. 

Letter from Alexandria on the evidence of the practical appli- 
cation of the quadrature of the circle in the great pyramids of 
Gizeh. By H. C. Agnew, 1 Esq. London, 1838, 4to. 

1 He seems to have written nothing else. If one wishes to enter 
into the subject of the mathematics of the Great Pyramid there is 
an extensive literature awaiting him. Richard William Howard Vyse 
(1784-1853) published in 1840 his Operations carried on at the Pyra- 
mids of Gieeh in 1837, and in this he made a beginning of a scien- 
tific metrical study of the subject. Charles Piazzi Smyth (1819- 
1900), astronomer Royal for Scotland (1845-1888) was much carried 
away with the number mysticism of the Great Pyramid, so much so that 
he published in 1864 a work entitled Our Inheritance in the Great 
Pyramid, in which his vagaries were set forth. Although he was 
then a Fellow of the Royal Society (1857), his work was so ill re- 
ceived that when he offered a paper on the subject it was rejected 
(1874) and he resigned in consequence of this action. The latest 
and perhaps the most scholarly of all investigators of the subject 
is William Matthew Flinders Petrie (born in 1853), Edwards pro- 
fessor of Egyptology at University College, London, whose Pyra- 
mids and Temples of Gizeh (1883) and subsequent works are justly 
esteemed as authorities. 



THE MATHEMATICS OF A CREED. 329 

Mr. Agnew detects proportions which he thinks were 
suggested by those of the circumference and diameter of a 
circle. 

THE MATHEMATICS OF A CREED. 

The creed of St. Athanasius proved by a mathematical parallel. 
Before you censure, condemn, or approve; read, examine, and 
understand. E. B. REViLO. 1 London, 1839, 8vo. 

This author really believed himself, and was in earnest. 
He is not the only person who has written nonsense by con- 
founding the mathematical infinite (of quantity) with what 
speculators now more correctly express by the unlimited, 
the unconditioned, or the absolute. This tract is worth 
preserving, as the extreme case of a particular kind. The 
following is a specimen. Infinity being represented by 00, 
as usual, and /, s, g, being finite integers, the three Persons 
are denoted by oo^ (woo)*, oo^ the finite fraction m repre- 
senting human nature, as opposed to oo. The clauses of the 
Creed are then given with their mathematical parallels. I 
extract a couple : 

"But the Godhead of the "It has been shown that 
Father, of the Son, and of oo/, cos, and (wOO)*, to- 
the Holy Ghost, is all one: gether, are but 00, and that 
the glory equal, the Majesty each is oo, and any magni- 
co-eternal. tude in existence represented 

kby 00 always was and al- 
ways will be: for it cannot 
be made, or destroyed, and 
yet exists. 
*As De Morgan subsequently found, this name reversed be- 
comes Oliver B...e, for Oliver Byrne, one of the odd characters 
among the minor mathematical writers of the middle of the last 
century. One of his most curious works is The first six Books of 
the Elements of Euclid; in which coloured diagrams and symbols 
are used instead of letters (1847). There is some merit in speak- 
ing of the red triangle instead of the triangle ABC, but not enough 
to give the method any standing. His Dual Arithmetic (1863-1867) 
was also a curious work. 



330 A BUDGET OF PARADOXES. 

"Equal to the Father, as "(wOO)* is equal to oof as 

touching his Godhead: and touching 00, but inferior to 

inferior to the Father, as cof as touching m: because 

touching his Manhood." m is not infinite." 

I might have passed this over, as beneath even my 
present subject, but for the way in which I became ac- 
quainted with it. A bookseller, not the publisher, handed 
it to me over his counter: one who had published mathe- 
matical works. He said, with an air of important communi- 
cation, Have you seen this, Sir! In reply, I recommended 

him to show it to my friend Mr. , for whom he had 

published mathematics. Educated men, used to books and to 
the converse of learned men, look with mysterious wonder 
on such productions as this : for which reason I have made 
a quotation which many will judge had better have been 
omitted. But it would have been an imposition on the pub- 
lic if I were, omitting this and some other uses of the 
Bible and Common Prayer, to pretend that I had given a 
true picture of my school. 

[Since the publication of the above, it has been stated 
that the author is Mr. Oliver Byrne, the author of the Dual 
Arithmetic mentioned further on: E. B. Revilo seems to be 
obviously a reversal.] 

LOGIC HAS NO PARADOXERS. 

Old and new logic contrasted : being an attempt to elucidate, for 
ordinary comprehension, how Lord Bacon delivered the human 
mind from its 2,000 years' enslavement under Aristotle. By 
Justin Brenan. 1 London, 1839, I2mo. 

Logic, though the other exact science, has not had the 
sort of assailants who have clustered about mathematics. 
There is a sect which disputes the utility of logic, but there 
are no special points, like the quadrature of the circle, which 

1 Brenan also wrote on English composition (1829), a work that 
went through fourteen editions by 1865 ; a work entitled The For- 
eigner's English Conjugator (1831), and a work on the national 
debt. 



LOGIC HAS NO PARADOXERS. 331 

excite dispute among those who admit other things. The 
old story about Aristotle having one logic to trammel us, 
and Bacon another to set us free, always laughed at by 
those who really knew either Aristotle or Bacon, now 
begins to be understood by a large section of the educated 
world. The author of this tract connects the old logic with 
the indecencies of the classical writers, and the new with 
moral purity: he appeals to women, who, "when they see 
plainly the demoralizing tendency of syllogistic logic, they 
will no doubt exert their powerful influence against it, and 
support the Baconian method." This is the only work 
against logic which I can introduce, but it is a rare one, I 
mean in contents. I quote the author's idea of a syllogism : 

"The basis of this system is the syllogism. This is a 
form of couching the substance of your argument or in- 
vestigation into one short line or sentence then corrobo- 
rating or supporting it in another, and drawing your con- 
clusion or proof in a third." 

On this definition he gives an example, as follows : "Every 
sin deserves death," the substance of the "argument or in- 
vestigation." Then comes, "Every unlawful wish is a sin," 
which "corroborates or supports" the preceding: and, lastly, 
"therefore every unlawful wish deserves death," which is 
the "conclusion or proof." We learn, also, that "sometimes 
the first is called the premises (sic), and sometimes the 
first premiss"; as also that "the first is sometimes called 
the proposition, or subject, or affirmative, and the next the 
predicate, and sometimes the middle term." To which is 
added, with a mark of exclamation at the end, "but in ana- 
lyzing the syllogism, there is a middle term, and a predicate 
too, in each of the lines!" It is clear that Aristotle never 
enslaved this mind. 

I have said that logic has no paradoxers, but I was 
speaking of old time. This science has slept until our own 
day: Hamilton 2 says there has been "no progress made in 

a See note 7, page 1 12. 



332 A BUDGET OF PARADOXES. 

the general development of the syllogism since the time of 
Aristotle ; and in regard to the few partial improvements, 
the professed historians seem altogether ignorant." But in 
our time, the paradoxer, the opponent of common opinion, 
has appeared in this field. I do not refer to Prof. Boole, 3 
who is not a paradoxer, but a discoverer: his system could 
neither oppose nor support common opinion, for its grounds 
were not in the conception of any one. I speak especially 
of two others, who fought like cat and dog: one was dog- 
matical, the other categorical. The first was Hamilton him- 
self Sir William Hamilton of Edinburgh, the metaphysi- 
cian,( not Sir William Rowan Hamilton* of Dublin, the 
mathematician J a combination of peculiar genius with un- 
precedented learning, erudite in all he could want except 
mathematics, for which he had no turn, and in which he 
had not even a schoolboy's knowledge, thanks to the Oxford 
of his younger day. The other was the author of this 
work, so fully described in Hamilton's writings that there 
is no occasion to describe him here. I shall try to say a few 
words in common language about the paradoxers. 

Hamilton's great paradox was the quantification of the 
predicate; a fearful phrase, easily explained. We all know 
that when we say "Men are animals/' a form wholly un- 
quantified in phrase, we speak of all men, but not of all 
animals: it is some or all, some may be all for aught the 
proposition says. This some-may-be-all-for-aught-we-say, 
or not-none, is the logician's some. One would suppose 

8 See note 2, page 261. 

*Sir William Rowan Hamilton (1805-1865), the discoverer of 
quaternions (1852), was an infant prodigy, competing with Zerah 
Colburn as a child. He was a linguist of remarkable powers, being 
able, at thirteen years of age, to boast that he knew as many languages 
as he had lived years. When only sixteen he found an error in 
Laplace's Mecanique celeste. When only twenty-two he was ap- 
pointed Andrews professor of astronomy, and he soon after became 
Astronomer Royal of Ireland. He was knighted in 1835. His earlier 
work was on optics, his Theory of Systems of Rays appearing in 
1823. In 1827 he published a paper on the principle of Varying Ac* 
tion. He also wrote on dynamics. 



LOGIC HAS NO PARADOXERS. 333 

that "all men are some animals," would have been the log- 
ical phrase in all time: but the predicate never was quanti- 
fied. The few who alluded to the possibility of such a thing 
found reasons for not adopting it over and above the great 
reason, that Aristotle did not adopt it. For Aristotle never 
ruled in physics or metaphysics in the old time with near so 
much of absolute sway as he has ruled in logic down to our 
own time. The logicians knew that in the proposition "all 
men are animals" the "animal" is not universal, but particu- 
lar yet no one dared to say that all men are some animals, 
and to invent the phrase, "some animals are all men" until 
Hamilton leaped the ditch, and not only completed a system 
of enunciation, but applied it to syllogism. 

My own case is as peculiar as his: I have proposed to 
introduce mathematical thought into logic to an extent which 
makes the old stagers cry: 

"St. Aristotle ! what wild notions ! 
Serve a ne exeat regno 6 on him !" 

Hard upon twenty years ago, a friend and opponent 
who stands high in these matters, and who is not nearly 
such a sectary of Aristotle and establishment as most, wrote 
to me as follows : "It is said that next to the man who forms 
the taste of the nation, the greatest genius is the man who 
corrupts it. I mean therefore no disrespect, but very much 
the reverse, when I say that I have hitherto always consid- 
ered you as a great logical heresiarch." Coleridge says he 
thinks that it was Sir Joshua Reynolds who made the re- 
mark: which, to copy a bull I once heard, I cannot deny, 
because I was not there when he said it. My friend did not 
call me to repentance and reconciliation with the church: 
I think he had a guess that I was a reprobate sinner. My 
offences at that time were but small: I went on spinning 
syllogism systems, all alien from the common logic, until I 
had six, the initial letters of which, put together, from the 

8 "Let him not leave the kingdom," a legal phrase. 



334 A BUDGET OF PARADOXES. 

names I gave before I saw what they would make, bar all 
repentance by the words 

RUE NOT! 

leaving to the followers of the old school the comfortable 
option of placing the letters thus: 

TRUE? NO! 

It should however be stated that the question is not 
about absolute truth or falsehood. No one denies that any- 
thing I call an inference is an inference: they say that my 
alterations are extra-logical-, that they are material, not 
formal', and that logic is a formal science. 

The distinction between material and formal is easily 
made, where the usual perversions are not required. A form 
is an empty machine, such as "Every X is Y"; it may be 
supplied with matter, as in "Every man is animal" The 
logicians will not see that their formal proposition, "Every 
X is Y," is material in three points, the degree of assertion, 
the quantity of the proposition, and the copula. The purely 
formal proposition is "There is the probability a that X 
stands in the relation L to Y." The time will come when it 
will be regretted that logic went without paradoxers for 
two thousand years: and when much that has been said on 
the distinction of form and matter will breed jokes. 

I give one instance of one mood of each of the systems, 
in the order of the letters first written above. 

Relative. In this system the formal relation is taken, 
that is, the copula may be any whatever. As a material in- 
stance, in which the relations are those of consanguinity (of 
men understood), take the following: X is the brother of 
Y ; X is not the uncle of Z ; therefore, Z is not the child of 
Y. The discussion of relation, and of the objections to the 
extension, is in the Cambridge Transactions, Vol. X, Part 2 ; 
a crabbed conglomerate. 

Undecided. In this system one premise, and want of 
power over another, infer want of power over a conclusion. 



LOGIC HAS NO PARADOXERS. 335 

As "Some men are not capable of tracing consequences ; we 
cannot be sure that there are beings responsible for conse- 
quences who are incapable of tracing consequences; there- 
fore, we cannot be sure that all men are responsible for the 
consequences of their actions." 

Exemplar. This, long after it suggested itself to me as 
a means of correcting a defect in Hamilton's system, I saw 
to be the very system of Aristotle himself, though his fol- 
lowers have drifted into another. It makes its subject and 
predicate examples, thus: Any one man is an animal; any 
one animal is a mortal ; therefore, any one man is a mortal. 

Numerical. Suppose 100 Ys to exist: then if 70 Xs 
be Ys, and 40 Zs be Ys, it follows that 10 Xs (at least) are 
Zs. Hamilton, whose mind could not generalize on sym- 
bols, saw that the word most would come under this system, 
and admitted, as valid, such a syllogism as "most Ys are 
Xs; most Ys are Zs; therefore, some Xs are Zs." 

Onymatic. This is the ordinary system much enlarged 
in prepositional forms. It is fully discussed in my Syllabus 
of Logic. 

Transposed. In this syllogism the quantity in one prem- 
ise is transposed into the other. As, some Xs are not Ys; 
for every X there is a Y which is Z ; therefore, some Zs are 
not Xs. 

Sir William Hamilton of Edinburgh was one of the best 
friends and allies I ever had. When I first began to publish 
speculation on this subject, he introduced me to the logical 
world as having plagiarized from him. This drew their 
attention: a mathematician might have written about logic 
under forms which had something of mathematical look 
long enough before the Aristotelians would have troubled 
themselves with him: as was done by John Bernoulli, 6 

Probably De Morgan is referring to Johann Bernoulli III (1744- 
1807), who edited Lambert's Logische und philosophische Abhand- 
lungen, Berlin, 1782. He was astronomer of the Academy of Sci- 
ences at Berlin. 



336 A BUDGET OF PARADOXES. 

James Bernoulli, 7 Lambert, 8 and Gergonne ; who, when our 
discussion began, were not known even to omnilegent Ham- 
ilton. He retracted his accusation of wilful theft in a manly 
way when he found it untenable; but on this point he 
wavered a little, and was convinced to the last that I had 
taken his principle unconsciously. He thought I had done 
the same with Ploucquet 10 and Lambert. It was his pet 
notion that I did not understand the commonest principles of 
logic, that I did not always know the difference between the 
middle term of a syllogism and its conclusion. It went 
against his grain to imagine that a mathematician could be 
a logician. So long as he took me to be riding my own 
hobby, he laughed consumedly: but when he thought he 
could make out that I was mounted behind Ploucquet or 
Lambert, the current ran thus : "It would indeed have been 
little short of a miracle had he, ignorant even of the common 
principles of logic, been able of himself to rise to generali- 
zation so lofty and so accurate as are supposed in the pecu- 
liar doctrines of both the rival logicians, Lambert and 
Ploucquet how useless soever these may in practice prove 
to be." All this has been sufficiently discussed elsewhere: 
"but, masters, remember that I am an ass." 

I know that I never saw Lambert's work until after all 
Hamilton supposed me to have taken was written: he him- 
self, who read almost everything, knew nothing about it 
until after I did. I cannot prove what I say about my 
knowledge of Lambert : but the means of doing it may turn 
up. For, by the casual turning up of an old letter, I have 

T Jacob Bernoulli (1654-1705) was one of the two brothers who 
founded the famous Bernoulli family of mathematicians, the other 
being Johann I. His Ars conjectandi (1713), published posthu- 
mously, was the first distinct treatise on probabilities. 

'Johann Heinrich Lambert (1728-1777) was one of the most 
learned men of his time. Although interested chiefly in mathematics, 
he wrote also on science, logic, and philosophy. 

'Joseph Diez Gergonne (1771-1859), a soldier under Napoleon, 
and founder of the Annalcs de mathematiques (1810). 

"Gottfried Ploucquet (1716-1790) was at first a clergyman, but 
afterwards became professor of logic at Tubingen. 



LOGIC HAS NO PARADOXERS. 337 

found the means of clearing myself as to Ploucquet. Ham- 
ilton assumed that (unconsciously) I took from Ploucquet 
the notion of a logical notation in which the symbol of the 
conclusion is seen in the joint symbols of the premises. For 
example, in my own fashion I write down ( . ) ( . ), two 
symbols of premises. By these symbols I see that there is 
a valid conclusion, and that it may be written in symbol by 
striking out the two middle parentheses, which gives ( . . ) 
and reading the two negative dots as an affirmative. And 
so I see in ( . ) ( . ) that ( ) is the conclusion. This, 
in full, is the perception that "all are either Xs or Ys" and 
"all are either Ys or Zs" necessitates "some Xs are Zs." 
Now in Ploucquet's book of 1763, is found, "Deleatur in 
praemissis medius ; id quod restat indicat conclusionem." 11 
In the paper in which I explain my symbols which are 
altogether different from Ploucquet's there is found "Erase 
the symbols of the middle term; the remaining symbols 
show the inference." There is very great likeness: and I 
would have excused Hamilton for his notion if he had fairly 
given reference to the part of the book in which his quota- 
tion was found. For I had shown in my Formal Logic what 
part of Ploucquet's book I had used: and a fair disputant 
would either have strengthened his point by showing that 
I had been at his part of the book, or allowed me the ad- 
vantage of it being apparent that I had not given evidence 
of having seen that part of the book. My good friend, 
though an honest man, was sometimes unwilling to allow 
due advantage to controversial opponents. 

But to my point. The only work of Ploucquet I ever 
saw was lent me by my friend Dr. Logan, 12 with whom I 
have often corresponded on logic, etc. I chanced (in 1865) 

1 "In the premises let the middle term be omitted ; what remains 
indicates the conclusion." 

"Probably Sir William Edmond Logan (1789-1875), who be- 
came so interested in geology as to be placed at the head of the geo- 
logical survey of Canada (1842). The University of Montreal con- 
ferred the title LL.D. upon him, and Napoleon III gave him the 
cross of the Legion of Honor. 



338 A BUDGET OF PARADOXES. 

to turn up the letter which he sent me (Sept. 12, 1847) with 
the book. Part of it runs thus: "I congratulate you on 
your success in your logical researches [that is, in asking 
for the book, I had described some results]. Since the 
reading of your first paper I have been satisfied as to the 
possibility of inventing a logical notation in which the 
rationale of the inference is contained in the symbol, though 
I never attempted to verify it [what I communicated, then, 
satisfied the writer that I had done and communicated what 
he, from my previous paper, suspected to be practicable]. 
I send you Ploucquet's dissertation ' 

It now being manifest that I cannot be souring grapes 
which have been taken from me, I will say what I never 
said in print before. There is not the slightest merit in 
making the symbols of the premises yield that of the con- 
clusion by erasure : the thing must do itself in every system 
which symbolizes quantities. For in every syllogism (ex- 
cept the inverted Bramantip of the Aristotelians) the con- 
clusion is manifest in this way without symbols. This 
Bramantip destroys system in the Aristotelian lot: and cir- 
cumstances which I have pointed out destroy it in Hamil- 
ton's own collection. But in that enlargement of the re- 
puted Aristotelian system which I have called onymatic, 
and in that correction of Hamilton's system which I have 
called exemplar, the rule of erasure is universal, and may 
be seen without symbols. 

Our first controversy was in 1846. In 1847, in my 
Formal Logic, I gave him back a little satire for satire, 
just to show, as I stated, that I could employ ridicule if I 
pleased. He was so offended with the appendix in which 
this was contained, that he would not accept the copy of the 
book I sent him, but returned it. Copies of controversial 
works, sent from opponent to opponent, are not presents, in 
the usual sense : it was a marked success to make him angry 
enough to forget this. It had some effect however: during 
the rest of his life I wished to avoid provocation; for I 



LOGIC HAS NO PARADOXERS. 339 

could not feel sure that excitement might not produce con- 
sequences. I allowed his slashing account of me in the 
Discussions to pass unanswered : and before that, when he 
proposed to open a controversy in the Athenceum upon my 
second Cambridge paper, I merely deferred the dispute until 
the next edition of my Formal Logic. I cannot expect the 
account in the Discussions to amuse an unconcerned reader 
as much as it amused myself: but for a cut-and-thrust, 
might-and-main, tooth-and-nail, hammer-and-tongs assault, 
I can particularly recommend it. I never knew, until I read 
it, how much I should enjoy a thundering onslought on 
myself, done with racy insolence by a master hand, to whom 
my good genius had whispered Ita feri ut se sentiat emori. 
Since that time I have, as the Irishman said, become "dry 
moulded for want of a bating." Some of my paradoxers 
have done their best: but theirs is mere twopenny "small 
swipes," as Peter Peebles said. Brandy for heroes ! I hope a 
reviewer or two will have mercy on me, and will give me as 
good discipline as Strafford would have given Hampden 
and his set: "much beholden," said he, "should they be to 
any one that should thoroughly take pains with them in 
that kind" meaning objective flagellation. And I shall 
be the same to any one who will serve me so but in a 
literary and periodical sense: my corporeal cuticle is as 
thin as my neighbors'. 

Sir W. H. was suffering under local paralysis before 
our controversy commenced: and though his mind was 
quite unaffected, a retort of as downright a character as the 
attack might have produced serious effect upon a person 
who had shown himself sensible of ridicule. Had a second 
attack of his disorder followed an answer from me, I should 
have been held to have caused it : though, looking at Hamil- 
ton's genial love of combat, I strongly suspected that a 
retort in kind 

u "So strike that he may think himself to die." 



340 A BUDGET OF PARADOXES. 

"Would cheer his heart, and warm his blood, 
And make him fight, and do him good." 

But I could not venture to risk it. So all I did, in reply to 
the article in the Discussions, was to write to him the follow- 
ing note: which, as illustrating an etiquette of controversy, 
I insert. 

"I beg to acknowledge and thank you for. . . It is neces- 
sary that I should say a word on my retention of this work, 
with reference to your return of the copy of my Formal 
Logic, which I presented to you on its publication : a return 
made on the ground of your disapproval of the account of 
our controversy which that work contained. According to 
my view of the subject, any one whose dealing with the 
author of a book is specially attacked in it, has a right to 
expect from the author that part of the book in which the 
attack is made, together with so much of the remaining part 
as is fairly context. And I hold that the acceptance by the 
party assailed of such work or part of a work does not imply 
any amount of approval of the contents, or of want of dis- 
approval. On this principle (though I am not prepared 
to add the word alone) I forwarded to you the whole of my 
work on Formal Logic and my second Cambridge Memoir. 
And on this principle I should have held you wanting in due 
regard to my literary rights if you had not forwarded to 
me your asterisked pages, with all else that was necessary 
to a full understanding of their scope and meaning, so far 
as the contents of the book would furnish it. For the re- 
maining portion, which it would be a hundred pities to sepa- 
rate from the pages in which I am directly concerned, I am 
your debtor on another principle; and shall be glad to re- 
main so if you will allow me to make a feint of balancing 
the account by the offer of two small works on subjects as 
little connected with our discussion as the Epistolce Ob- 
scurorum Virorum, or the Lutheran dispute. I trust that 
by accepting my Opuscula you will enable me to avoid the 



SOME DOGGEREL AND COUNTER DOGGEREL. 341 

use of the knife, and leave me to cut you up with the pen as 
occasion shall serve, I remain, etc. (April 21, 1852)." 

I received polite thanks, but not a word about the body 
of the letter: my argument, I suppose, was admitted. 

SOME DOGGEREL AND COUNTER DOGGEREL. 

I find among my miscellaneous papers the following 
jeu d' esprit, or jeu de betise* whichever the reader pleases 
I care not intended, before I saw ground for abstaining, 
to have, as the phrase is, come in somehow. I think I could 
manage to bring anything into anything: certainly into a 
Budget of Paradoxes. Sir W. H. rather piqued himself upon 
some caniculars, or doggerel verses, which he had put to- 
gether in memoriam [technicam] of the way in which 
A E I O are used in logic : he added U, Y, for the addition 
of meet, etc., to the system. I took the liberty of concocting 
some counter-doggerel, just to show that a mathematician 
may have architectonic power as well as a metaphysician. 

DOGGEREL. 
BY SIR W. HAMILTON. 

A it affirms of this, these, all, 

Whilst E denies of any; 
I it affirms (whilst O denies) 

Of some (or few, or many). 

Thus A affirms, as E denies, 

And definitely either; 
Thus I affirms, as O denies, 

And definitely neither. 

A half, left semidefinite, 

Is worthy of its score ; 
U, then, affirms, as Y denies, 

This, neither less nor more. 

Indefinito-definites, 
I, UI, YO, last we come; 

1 "Witticism or piece of stupidity." 



342 A BUDGET OF PARADOXES. 

And this affirms, as that denies 
Of more, most (half, plus, some). 

COUNTER DOGGEREL. 

BY PROF. DE MORGAN. 

(1847.) 

GREAT A affirms of all; 

Sir William does so too: 
When the subject is "my suspicion," 

And the predicate "must be true." 

Great E denies of all ; 

Sir William of all but one: 
When he speaks about this present time, 

And of those who in logic have done. 

Great I takes up but some-, 

Sir William! my dear soul! 
Why then in all your writings, 

Does "Great I" fill 2 the whole! 

Great O says some are not; 

Sir William's readers catch, 
That some (modern) Athens is not without 

An Aristotle to match. 

"A half, left semi-definite, 

Is worthy of its score:" 
This looked very much like balderdash, 

And neither less nor more. 

It puzzled me like anything; 

In fact, it puzzled me worse: 
Isn't schoolman's logic hard enough, 

Without being in Sibyl's verse? 

S A very truculently unjust assertion: for Sir W. was as great 
a setter up of some as he was a puller down of others. His writings 
are a congeries of praises and blames, both cruel smart, as they say 
in the States. But the combined instigation of prose, rhyme, and 
retort would send Aristides himself to Tartarus, if it were not pretty 
certain that Minos would grant a stet processus under the circum- 
stances. The first two verses are exaggerations standing on a basis 
of truth. ^ The fourth verse is quite true : Sir W. H. was an Edin- 
burgh Aristotle, with the difference of ancient and modern Athens 
well marked, especially the perfervidum ingenium Scotorum. 
A. De M. 






SOME DOGGEREL AND COUNTER DOGGEREL. 343 

At last, thinks I, 'tis German; 

And I'll try it with some beer ! 
The landlord asked what bothered me so, 

And at once he made it clear. 

It's half-and-half, the gentleman means ; 

Don't you see he talks of score? 
That's the bit of memorandum 

That we chalk behind the door. 

Semi-definite 's outlandish ; 

But I see, in half a squint, 
That he speaks of the lubbers who call for a quart, 

When they can't manage more than a pint. 

Now I'll read it into English, 
And then you'll answer me this : 

If it isn't good logic all the world round, 
I should like to know what is? 

When you call for a pot of half-and-half, 
If you're lost to sense of shame, 

You may leave it semi-definite, 
But you pay for it all just the same. 
* * * * 

I am unspeakably comforted when I look over the above 
in remembering that the question is not whether it be Pin- 
daric or Horatian, but whether the copy be as good as the 
original. And I say it is : and will take no denial. 

Long live long will live the glad memory of William 
Hamilton, Good, Learned, Acute, and Disputatious! He 
fought upon principle: the motto of his book is: 

"Truth, like a torch, the more it's shook it shines." 

There is something in this; but metaphors, like puddings, 
quarrels, rivers, and arguments, always have two sides to 
them. For instance, 

"Truth, like a torch, the more it's shook it shines ; 

But those who want to use it, hold it steady. 
They shake the flame who like a glare to gaze at, 
They keep it still who want a light to see by." 



344 A BUDGET OF PARADOXES. 



ANOTHER THEORY OF PARALLELS. 

Theory of Parallels. The proof of Euclid's axiom looked for in 
the properties of the Equiangular Spiral. By Lieut-Col. G. 
Perronet Thompson. 1 The same, second edition, revised and 
corrected. The same, third edition, shortened, and freed from 
dependence on the theory of limits. The same, fourth edition, 
ditto, ditto. All London, 1840, Svo. 

To explain these editions it should be noted that General 
Thompson rapidly modified his notions, and republished his 
tracts accordingly. 

SOME PRIMITIVE DARWINISM. 

Vestiges of the Natural History of Creation. 1 London, 1840, 
I2mo. 

This is the first edition of this celebrated work. Its 
form is a case of the theory : the book is an undeniable duo- 
decimo, but the size of its paper gives it the look of not the 
smallest of octavos. Does not this illustrate the law of 
development, the gradation of families, the transference of 
species, and so on? If so, I claim the discovery of this 
esoteric testimony of the book to its own contents ; I defy 
any one to point out the reviewer who has mentioned it. 
The work itself is decribed by its author as "the first at- 
tempt to connect the natural sciences into a history of 
creation." The attempt was commenced, and has been 
carried on, both with marked talent, and will be continued. 
Great advantage will result: at the worst we are but in the 
alchemy of some new chemistry, or the astrology of some 
new astronomy. Perhaps it would be as well not to be 
too sure on the matter, until we have an antidote to possible 
consequences as exhibited under another theory, on which 

1 See note 2, p. 252. There was also a Theory of Parallels that dif- 
fered from these, London, 1853, second edition 1856, third edition 1856. 

/The work was written by Robert Chambers (1802-1871), the 
Edinburgh publisher, a friend of Scott and of many of his contem- 
poraries in the literary field. He published the Vestiges of the Nat- 
ural History of Creation in 1844, not 1840. 



ON RELIGIOUS INSURANCE. 345 

it is as reasonable to speculate as on that of the Vestiges. 
I met long ago with a splendid player on the guitar, who 
assured me, and was confirmed by his friends, that he 
never practised, except in thought, and did not possess an 
instrument: he kept his fingers acting in his mind, until 
they got their habits ; and thus he learnt the most difficult 
novelties of execution. Now what if this should be a 
minor segment of a higher law? What if, by constantly 
thinking of ourselves as descended from primeval monkeys, 
we should if it be true actually get our tails again ? What 
if the first man who was detected with such an appendage 
should be obliged to confess himself the author of the 
Vestiges a person yet unknown who would naturally 
get the start of his species by having had the earliest habit 
of thinking on the matter? I confess I never hear a man 
of note talk fluently about it without a curious glance at 
his proportions, to see whether there may be ground to 
conjecture that he may have more of "mortal coil" than 
others, in anaxyridical concealment. I do not feel sure that 
even a paternal love for his theory would induce him, in the 
case I am supposing, to exhibit himself at the British Asso- 
ciation, 

With a hole behind which his tail peeped through. 

The first sentence of this book (1840) is a cast of the log, 
which shows our rate of progress. "It is familiar knowl- 
edge that the earth which we inhabit is a globe of some- 
what less than 8,000 miles in diameter, being one of a 
series of eleven which revolve at different distances around 
the sun." The eleven\ Not to mention the Iscariot which 
Le Verrier and Adams calculated into existence, there is 
more than a septuagint of new planetoids. 

ON RELIGIOUS INSURANCE. 

The Constitution and Rules of the Ancient and Universal 'Bene- 
fit Society' established by Jesus Christ, exhibited, and its 
advantages and claims maintained, against all Modern and 



346 A BUDGET OF PARADOXES. 

merely Human Institutions of the kind : A Letter very respect- 
fully addressed to the Rev. James Everett, 1 and occasioned 
by certain remarks made by him, in a speech to the Members 
of the 'Wesleyan Centenary Institute' Benefit Society. Dated 
York, Dec. 7, 1840. By Thomas Smith. 2 I2mo, (pp. 8.) 

The Wesleyan minister addressed had advocated provision 
against old age, etc. : the writer declares all private provision 
tin-Christian. After decent maintenance and relief of fam- 
ily claims of indigence, he holds that all the rest is to go 
to the "Benefit Society," of which he draws up the rules, 
in technical form, with chapters of "Officers," "Contribu- 
tors" etc., from the Acts of the Apostles, etc., and some of 
the early Fathers. He holds that a Christian may not "make 
a private provision against the contingencies of the future" : 
and that the great "Benefit Society" is the divinely-ordained 
recipient of all the surplus of his income; capital, beyond 
what is necessary for business, he is to have none. A real 
good speculator shuts his eyes by instinct, when opening 
them would not serve the purpose: he has the vizor of the 
Irish fairy tale, which fell of itself over the eyes of the 
wearer the moment he turned them upon the enchanted light 
which would have destroyed him if he had caught sight 
of it. "Whiles it remained, was it not thine own? and 
after it was sold, was it (the purchase-money) not in thine 
own power?" would have been awkward to quote, and ac- 
cordingly nothing is stated except the well-known result, 
which is rule 3, cap. 5, "Prevention of Abuses." By putting 
his principles together, the author can be made, logically, 
to mean that the successors of the apostles should put to 
death all contributors who are detected in not paying their 
full premiums. 

Everett (1784-1872) was at that time a good Wesleyan, but was 
expelled from the ministry in 1849 for having written Wesleyan 
Takings and as under suspicion for having started the Fly Sheets 
in 1845. In 1857 he established the United Methodist Free Church. 

2 Smith was a Primitive Methodist preacher. He also wrote 
an Earnest Address to the Methodists (1841) and The Wealth 
Question (1840?). 



THE TWO OLD PARADOXES AGAIN. 347 

I have known one or two cases in which policy-holders 
have surrendered their policies through having arrived at 
a conviction that direct provision is unlawful. So far as 
I could make it out, these parties did not think it unlawful 
to lay by out of income, except when this was done in a 
manner which involved calculation of death-chances. It is 
singular they did not see that the entrance of chance of 
death was the entrance of the very principle of the benefit 
society described in the Acts of the Apostles. The family 
of the one who died young received more in proportion to 
premiums paid than the family of one who died old. Every 
one who understands life assurance sees that bonus apart 
the difference between an assurance office and a savings 
bank consists in the adoption, pro tanto, of the principle 
of community of goods. In the original constitution of 
the oldest assurance office, the Amicable Society, the plan 
with which they started was nothing but this: persons of 
all ages under forty-five paid one common premium, and the 
proceeds were divided among the representatives of those 
who died within the year. 

THE TWO OLD PARADOXES AGAIN. 

[I omitted from its proper place a manuscript quadra- 
ture (3.1416 exactly) addressed to an eminent mathemati- 
cian, dated in 1842 from the debtor's ward of a country 
gaol. The unfortunate speculator says, "I have labored 
many years to find the precise ratio." I have heard of sev- 
eral cases in which squaring the circle has produced an in- 
ability to square accounts. I remind those who feel a kind 
of inspiration to employ native genius upon difficulties, 
without gradual progression from elements, that the call 
is one which becomes stronger and stronger, and may lead, 
as it has led, to abandonment of the duties of life, and all 
the consequences.] 



348 A BUDGET OF PARADOXES. 

1842. Provisional Prospectus of the Double Acting Rotary 
Engine Company. Also Mechanic's Magazine, March 26, 
1842. 

Perpetual motion by a drum with one vertical half in 
mercury, the other in a vacuum : the drum, I suppose, work- 
ing round forever to find an easy position. Steam to be 
superseded : steam and electricity convulsions of nature 
never intended by Providence for the use of man. The 
price of the present engines, as old iron, will buy new en- 
gines that will work without fuel and at no expense. Guaran- 
teed by the Count de Predaval, 1 the discoverer. I was to 
have been a Director, but my name got no further than 
ink, and not so far as official notification of the honor, 
partly owing to my having communicated to the Mechan- 
ic's Magazine information privately given to me, which 
gave premature publicity, and knocked up the plan. 

An Exposition of the Nature, Force, Action, and other prop- 
erties of Gravitation on the Planets. London, 1842, I2mo. 

An Investigation of the principles of the Rules for determining 
the Measures of the Areas and Circumferences of Circular 
Plane Surfaces . . . London, 1844, 8vo. 

These are anonymous ; but the author (whom I believe 
to be Mr. Denison, 2 presently noted) is described as author 
of a new system of mathematics, and also of mechanics. He 
had need have both, for he shows that the line which has 
a square equal to a given circle, has a cube equal to the 
sphere on the same diameter : that is, in old mathematics, the 
diameter is to the circumference as 9 to 16 ! Again, admitting 
that the velocities of planets in circular orbits are inversely as 
the square roots of their distances, that is, admitting Kepler's 
law, he manages to prove that gravitation is inversely as 
the square root of the distance: and suspects magnetism 
of doing the difference between this and Newton's law. 

J He wrote the Nouveau traite de Balistique, Paris, 1837. 

8 Joseph Denison, known to fame only through De Morgan. 
See also page 353. 



THE DUPLICATION PROBLEM. 349 

Magnetism and electricity are, in physics, the member of 
parliament and the cabman at every man's bidding, as 
Henry Warburton 3 said. 

The above is an outrageous quadrature. In the pre- 
ceding year, 1841, was published what I suppose at first to 
be a Maori quadrature, by Maccook. But I get it from a 
cutting out of some French periodical, and I incline to 
think that it must be by a Mr. M'Cook. He makes TT to be 



THE DUPLICATION PROBLEM. 

Refutation of a Pamphlet written by the Rev. John Mackey, 
R.C.P., 1 entitled "A method of making a cube double of a 
cube, founded on the principles of elementary geometry," 
wherein his principles are proved erroneous, and the required 
solution not yet obtained. By Robert Murphy. 2 Mallow, 1824, 
I2mo. 

This refutation was the production of an Irish boy of 
eighteen years old, self-educated in mathematics, the son 
of a shoemaker at Mallow. He died in 1843, leaving a 
name which is well known among mathematicians. His 
works on the theory of equations and on electricity, and his 
papers in the Cambridge Transactions, are all of high 
genius. The only account of him which I know of is that 
which I wrote for the Supplement of the Penny Cyclopcedia. 
He was thrown by his talents into a good income at Cam- 
bridge, with no social training except penury, and very little 
intellectual training except mathematics. He fell into dissi- 
pation, and his scientific career was almost arrested: but 
he had great good in him, to my knowledge. A sentence in 

'The radical (1784?- 1858), advocate of the founding of London 
university (1826), of medical reform (1827-1834), and of the repeal 
of the duties on newspapers and corn, and an ardent champion of 
penny postage. 

1 I. e., Roman Catholic Priest. 

2 Murphy (1806-1843) showed extraordinary powers in mathe- 
matics even before the age of thirteen. He became a fellow of Caius 
College, Cambridge, in 1829, dean in 1831, and examiner in mathe- 
matics in London University in 1838. 



350 A BUDGET OF PARADOXES. 

a letter from the late Dean Peacock 3 to me giving some 
advice about the means of serving Murphy sets out the 
old case: "Murphy is a man whose special education is in 
advance of his general; and such men are almost always 
difficult subjects to manage." This article having been 
omitted in its proper place, I put it at 1843, the date of 
Murphy's death. 

A NEW VALUE OF -. 

The Invisible Universe disclosed; or, the real Plan and Govern- 
ment of the Universe. By Henry Coleman Johnson, Esq. 
London, 1843, 8vo. 

The book opens abruptly with: 

"First demonstration. Concerning the centre: showing 
that, because the centre is an innermost point at an equal 
distance between two extreme points of a right line, and 
from every two relative and opposite intermediate points, 
it is composed of the two extreme internal points of each 
half of the line; each extreme internal point attracting 
towards itself all parts of that half to which it belongs. . ." 

Of course the circle is squared : and the circumference is 
diameters. 

SOME MODERN ASTROLOGY. 

Combination of the Zodiacal and Cometical Systems. Printed 
for the London Society, Exeter Hall. Price Sixpence, (n. d. 
1843-) 

What this London Society was, or the "combination," 
did not appear. There was a remarkable comet in 1843, 
the tail of which was at first confounded with what is called 
the zodiacal light. This nicely-printed little tract, evidently 
got up with less care for expense than is usual in such 
works, brings together all the announcements of the as- 
tronomers, and adds a short head and tail piece, which I 
shall quote entire. As the announcements are very ordinary 

8 See note 2, page 196. 



SOME MODERN ASTROLOGY. 351 

astronomy, the reader will be able to detect, if detection be 
possible, what is the meaning and force of the "Combina- 
tion of the Zodiacal and Cometical Systems": 

"Premonition. It has pleased the AUTHOR of CREATION 
to cause (to His human and reasoning Creatures of this 
generation, by a 'combined' appearance in His Zodiacal and 
Cometical system) a 'warning Crisis' of universal concern- 
ment to this our GLOBE. It is this 'Crisis' that has so gen- 
erally 'ROUSED' at this moment the 'nations throughout the 
Earth' that no equal interest has ever before been excited 
by MAN ; unless it be in that caused by the ' PAGAN-TEMPLE 
IN ROME/ which is recorded by the elder Pliny, 'Nat. Hist/ 
i. 23. iii. 3. HARDOUIN." 

After the accounts given by the unperceiving astronomers, 
comes what follows: 

"Such has been (hitherto) the only object discerned by 
the Wise of this World,' in this twofold union of the 'Zo- 
diacal' and 'Cometical' systems : yet it is nevertheless a most 
'Thrilling Warning' to all the inhabitants of this precarious 
and transitory EARTH. We have no authorized intimation 
or reasonable prospective contemplation, of 'current time' 
beyond a year 1860, of the present century ; or rather, ex- 
cept 'the interval which may now remain from the present 
year 1843, to a year I860' (^ue'pas 'EEHKONTA 'threescore 
or sixty days' 7 have appointed each "DAY" for a "YEAR," ' 
Ezek. iv. 6) : and we know, from our 'common experience' 
how speedily such a measure of time will pass away. 

"No words can be 'more explicit than these of OUR 
BLESSED LORD: viz. THIS GOSPEL of the Kingdom shall be 
preached in ALL the EARTH, for a Witness to ALL NATIONS; 
AND THEN, shall the END COME/ The 'next 18 years' must 
therefore supply the interval of the 'special Episcopal fore- 
runners.' 

(Matt. xxiv. 14.) 

"See the 'JEWISH INTELLIGENCER' of the present month 
(April), p. 153, for the 'Debates in Parliament,' respecting 



352 A BUDGET OF PARADOXES. 

the BISHOP OF JERUSALEM, viz. Dr. Bowring, 1 Mr. Hume, 2 
Sir R. Inglis, 3 Sir R. Peel, 4 Viscount Palmerston. 5 " 

I have quoted this at length, to show the awful threats 
which were published at a time of some little excitement 
about the phenomenon, under the name of the London 
Society. The assumption of a corporate appearance is a 
very unfair trick: and there are junctures at which harm 
might be done by it. 

THE NUMBER OF THE BEAST. 

Wealth the name and number of the Beast, 666, in the Book of 
Revelation, [by John Taylor. 1 ] London, 1844, 8vo. 

Whether Junius or the Beast be the more difficult to 
identify, must be referred to Mr. Taylor, the only person 
who has attempted both. His cogent argument on the 
political secret is not unworthily matched in his treatment 
of the theological riddle. He sees the solution in cforopia, 
which occurs in the Acts of the Apostles as the word for 
wealth in one of its most disgusting forms, and makes 666 
in the most straightforward way. This explanation has as 
good a chance as any other. The work contains a general 

*Sir John Bowring (1792-1872), the linguist, writer, and trav- 
eler, member of many learned societies and a writer of high repu- 
tation in his time. His works were not, however, of genuine merit. 

3 Joseph Hume (1777-1855) served as a surgeon with the British 
army in India early in the nineteenth century. He returned to Eng- 
land in 1808 and entered parliament as a radical in 1812. He was 
much interested in all reform movements. 

'Sir Robert Harry Inglis (1786-1855), a strong Tory, known 
for his numerous addresses in the House of Commons rather than 
for any real ability. 

4 Sir Robert Peel (1788-1850) began his parliamentary career 
in 1809 and was twice prime minister. He was prominent in most of 
the great reforms of his time. 

B See note 5, page 290. 

1 John Taylor (1781-1864) was a publisher, and published several 
pamphlets opposed to Peel's currency measures. De Morgan refers 
to his work on the Junius question. This was done early in his 
career, and resulted in A Discovery of the author of the Letters of 
Junius (1813), and The Identity of Junius with a distinguished liv- 
ing character established (1816), this being Sir Philip Francis. 



EASTER DAY PARADOXERS. 353 

attempt at explanation of the Apocalypse, and some history 
of opinion on the subject. It has not the prolixity which 
is so common a fault of apocalyptic commentators. 

A practical Treatise on Eclipses. .. .with remarks on the anom- 
alies of the present Theory of the Tides. By T. Kerigan, 2 
F.R.S. 1844, 8vo. 

Containing also a refutation of the theory of the tides, 
and afterwards increased by a supplement, "Additional 
facts and arguments against the theory of the tides," in 
answer to a short notice in the Athenceum journal. Mr. 
Kerigan was a lieutenant in the Navy: he obtained ad- 
mission to the Royal Society just before the publication of 
his book. 

A new theory of Gravitation. By Joseph Denison, 3 Esq. Lon- 
don, 1844, I2mo. 

Commentaries on the Principia. By the author of 'A new theory 
of Gravitation.' London, 1846, 8vo. 

Honor to the speculator who can be put in his proper 
place by one sentence, be that place where it may. 

"But we have shown that the velocities are inversely as 
the square roots of the mean distances from the sun ; where- 
fore, by equality of ratios, the forces of the sun's gravita- 
tion upon them are also inversely as the square roots of their 
distances from the sun." 

EASTER DAY PARADOXERS. 

In the years 1818 and 1845 the full moon fell on Easter 
Day, having been particularly directed to fall before it in 
the act for the change of style and in the English missals 
and prayer-books of all time: perhaps it would be more 
correct to say that Easter Day was directed to fall after 
the full moon ; "but the principle is the same." No explana- 
tion was given in 1818, but Easter was kept by the tables, 

2 See note 5, page 308. 

3 See page 348. 



354 A BUDGET OF PARADOXES. 

in defiance of the rule, and of several protests. A chrono- 
logical panic was beginning in December 1844, which was 
stopped by the Times newspaper printing extracts from an 
article of mine in the Companion to the Almanac for 1845, 
which had then just appeared. No one had guessed the 
true reason, which is that the thing called the moon in the 
Gregorian Calendar is not the moon of the heavens, but 
a fictitious imitation put wrong on purpose, as will pres- 
ently appear, partly to keep Easter out of the way of the 
Jews' Passover, partly for convenience of calculation. The 
apparent error happens but rarely; and all the work will 
perhaps have to be gone over next time. I now give two 
bits of paradox. 

Some theologians were angry at this explanation. A 
review called the Christian Observer (of which Christian- 
ity I do not know) got up a crushing article against me. 
I did not look at it, feeling sure that an article on such a 
subject which appeared on January 1, 1845, against a 
publication made in December 1844, must be a second-hand 
job. But some years afterwards (Sept. 10, 1850), the re- 
views, etc. having been just placed at the disposal of readers 
in the old reading-room of the Museum, I made a tour of 
inspection, came upon my critic on his perch, and took a 
look at him. I was very glad to remember this, for, though 
expecting only second-hand, yet even of this there is good 
and bad; and I expected to find some hints in the good 
second-hand of a respectable clerical publication. I read 
on, therefore, attentively, but not long: I soon came to the 
information that some additions to Delambre's 1 statement 
of the rule for finding Easter, belonging to distant years, 
had been made by Sir Harris Nicolas! 2 Now as I myself 
furnished my friend Sir H. N. with Delambre's digest of 

1 See note 3, page 160. 

_ 2 Sir Nicholas Harris Nicolas (1799-1848) was a reformer in 
various lines, the Record Commission, the Society of Antiquaries, 
and the British Museum, and his work was not without good results. 



EASTER DAY PARADOXERS. 355' 

Clavius's 3 rule, which I translated out of algebra into com- 
mon language for the purpose, I was pretty sure this was 
the ignorant reading of a person to whom Sir H. N. was 
the highest arithmetical authority on the subject. A person 
pretending to chronology, without being able to distinguish 
the historical points so clearly as they stand out in which 
Sir H. N. speaks with authority, from the arithmetical 
points of pure reckoning on which he does not pretend to 
do more than directly repeat others, must be as fit to talk 
about the construction of Easter Tables as the Spanish are 
to talk French. I need hardly say that the additions for 
distant years are as much from Clavius as the rest: my 
reviewer was not deep enough in his subject to know that 
Clavius made and published, from his rules, the full table 
up to A. D. 5000, for all the movable feasts of every year ! 
I gave only a glance at the rest : I found I was either knave 
or fool, with a leaning to the second opinion; and I came 
away satisfied that my critic was either ignoramus or novice, 
with a leaning to the first. I afterwards found an ambiguity 
of expression in Sir H. N.'s account whether his or mine 
I could not tell which might mislead a novice or content 
an ignoramus, but would have been properly read or further 
inquired into by a competent person. 

The second case is this. Shortly after the publication 
of my article, a gentleman called at my house, and, finding 
I was not at home, sent up his card with a stylish west-end 
club on it to my wife, begging for a few words on pressing 
business. With many well-expressed apologies, he stated 
that he had been alarmed by hearing that Prof. De M. had 
an intention of altering Easter next year. Mrs. De M. kept 
her countenance, and assured him that I had no such inten- 
tion, and further, that she greatly doubted my having the 
power to do it. Was she quite sure ? his authority was very 
good: fresh assurances given. He was greatly relieved, 
for he had some horses training for after Easter, which 

3 See note 5, page 69. 



356 A BUDGET OF PARADOXES. 

would not be ready to run if it were altered the wrong way. 
A doubt comes over him : would Mrs. De M.. in the event 
of her being mistaken, give him the very earliest informa- 
tion ? Promise given ; profusion of thanks ; more apologies ; 
and departure. 

Now, candid reader! or uncandid either! which most 
deserves to be laughed at ? A public instructor, who under- 
takes to settle for the world whether a reader of Clavius, 
the constructor of the Gregorian Calendar, is fool or knave, 
upon information derived from a compiler in this matter 
of his own day ; or a gentleman of horse and dog associa- 
tions, who, misapprehending something which he heard 
about a current topic, infers that the reader of Clavius had 
the ear of the Government on a proposed alteration. I suppose 
the querist had heard some one say, perhaps, that the day 
ought to be set right, and some one else remark that I might 
be consulted, as the only person who had discussed the 
matter from the original source of the Calendar. 

To give a better chance of the explanation being at once 
produced, next time the real full moon and Easter Day shall 
fall together, I insert here a summary which was printed 
in the Irish Prayer-book of the Ecclesiastical Society. If 
the amusement given by paradoxers should prevent a use- 
less discussion some years hence, I and the paradoxers shall 
have done a little good between us at any rate, I have 
done my best to keep the heavy weight afloat by tying 
bladders to it. I think the next occurrence will be in 1875. 

EASTER DAY. 

In the years 1818 and 1845, Easter Day, as given by the 
rules in 24 Geo. II cap. 23. (known as the act for the 
change of style) contradicted the precept given in the pre- 
liminary explanations. The precept is as follows: 

"Easter Day, on which the rest" of the moveable feasts 
"depend, is always the First Sunday after the Full Moon, 
which happens upon or next after the Twenty-first Day of 



EASTER DAY PARADOXERS. 357 

March] and if the Full Moon happens upon a Sunday, 
Easter Day is the Sunday after." 

But in 1818 and 1845, the full moon fell on a Sunday, 
and yet the rules gave that same Sunday for Easter Day. 
Much discussion was produced by this circumstance in 1818 : 
but a repetition of it in 1845 was nearly altogether prevented 
by a timely 4 reference to the intention of those who con- 
ducted the Gregorian reformation of the Calendar. Never- 
theless, seeing that the apparent error of the Calendar is 
due to the precept in the Act of Parliament, which is both 
erroneous and insufficient, and that the difficulty will recur 
so often as Easter Day falls on the day of full moon, it may 
be advisable to select from the two articles cited in the note 
such of their conclusions and rules, without proof or con- 
troversy, as will enable the reader to understand the main 
points of the Easter question, and, should he desire it, to 
calculate for himself the Easter of the old or new style, for 
any given year. 

1. In the very earliest age of Christianity, a controversy 
arose as to the mode of keeping Easter, some desiring to 
perpetuate the Passover, others to keep the festival of the 
Resurrection. The first afterwards obtained the name of 
Quartadecimans, from their Easter being always kept on 
the fourteenth day of the moon (Exod. xii. 18, Levit. xxiii. 
5.). But though it is unquestionable that a Judaizing party 
existed, it is also likely that many dissented on chrono- 
logical grounds. It is clear that no perfect anniversary can 
take place, except when the fourteenth of the moon, and 
with it the passover, falls on a Friday. Suppose, for in- 
stance, it falls on a Tuesday: one of three things must be 

*In the Companion to the Almanac for 1845 is a paper by Prof. 
De Morgan, "On the Ecclesiastical Calendar," the statements of 
which, so far as concerns the Gregorian Calendar, are taken direct 
from the work of Clavius, the principal agent in the arrangement of 
the reformed reckoning. This was followed, in the Companion to the 
Almanac for 1846, by a second paper, by the same author, headed 
"On the Earliest Printed Almanacs," much of which is written in 
direct supplement to the former article. S. E. De Morgan. 



358 A BUDGET OF PARADOXES. 

done. Either (which seems never to have been proposed) 
the crucifixion and resurrection must be celebrated on Tues- 
day and Sunday, with a wrong interval ; or the former on 
Tuesday, the latter on Thursday, abandoning the first day 
of the week; or the former on Friday, and the latter on 
Sunday, abandoning the paschal commemoration of the cru- 
cifixion. 

The last mode has been, as every one knows, finally 
adopted. The disputes of the first three centuries did not 
turn on any calendar questions. The Easter question was 
merely the symbol of the struggle between what we may 
call the Jewish and Gentile sects of Christians : and it nearly 
divided the Christian world, the Easterns, for the most part, 
being Quartadecimans. It is very important to note that 
there is no recorded dispute about a method of predicting 
the new moon, that is, no general dispute leading to forma- 
tion of sects: there may have been difficulties, and discus- 
sions about them. The Metonic cycle, presently mentioned, 
must have been used by many, perhaps most, churches. 

2. The question came before the Nicene Council (A. D. 
325) not as an astronomical, but as a doctrinal, question: 
it was, in fact, this, Shall the passover* be treated as a part 
of Christianity? The Council resolved this question in the 
negative, and the only information on its premises and con- 
clusion, or either, which comes from itself, is contained in 
the following sentence of the synodical epistle, which epistle 
is preserved by Socrates 6 and Theodoret. 7 "We also send 

5 It may be necessary to remind some English readers that in 
Latin and its derived European languages, what we call Easter is 
called the passover (pascha). The Quartadecimans had the name 
on their side : a possession which often is, in this world, nine points 
of the law. A. De M. 

fl Socrates Scholasticus was born at Constantinople c. 379, and 
died after 439. His Historia Ecclesiastic a (in Greek) covers the 
period from Constantine the Great to about 439, and includes the 
Council of Nicaea. The work was printed in Paris 1544. 

7 Theodoretus or Theodoritus was born at Antioch and died 
about 457. He was one of the greatest divines of the fifth century, 
a man of learning, piety, and judicial mind, and a champion of free- 
dom of opinion in all religious matters. 



EASTER DAY PARADOXERS. 359 

you the good news concerning the unanimous consent of all 
in reference to the celebration of the most solemn feast of 
Easter, for this difference also has been made up by the 
assistance of your prayers: so that all the brethren in the 
East, who formerly celebrated this festival at the same 
time as the Jews, will in future conform to the Romans and 
to us, and to all who have of old observed our manner of 
celebrating Easter." This is all that can be found on the 
subject: none of the stories about the Council ordaining 
the astronomical mode of finding Easter, and introducing 
the Metonic cycle into ecclesiastical reckoning, have any 
contemporary evidence: the canons which purport to be 
those of the Nicene Council do not contain a word about 
Easter; and this is evidence, whether we suppose those 
canons to be genuine or spurious. 

3. The astronomical dispute about a lunar cycle for the 
prediction of Easter either commenced, or became prom- 
inent, by the extinction of greater ones, soon after the time 
of the Nicene Council. Pope Innocent I 8 met with difficulty 
in 414. S. Leo, 9 in 454, ordained that Easter of 455 should 
be April 24; which is right. It is useless to record details 
of these disputes in a summary: the result was, that in the 
year 463, Pope Hilarius 10 employed Victorinus 11 of Aqui- 
taine to correct the Calendar, and Victorinus formed a rule 
which lasted until the sixteenth century. He combined the 
Metonic cycle and the solar cycle presently described. But 

8 He died in 417. He was a man of great energy and of high 
attainments. 

9 He died in 461, having reigned as pope for twenty-one years. 
It was he who induced Attila to spare Rome in 452. 

10 He succeeded Leo as pope in 461, and reigned for seven years. 

"Victorinus or Victorius Marianus seems to have been born at 
Limoges. He was a mathematician and astronomer, and the cycle 
mentioned by De Morgan is one of 532 years, a combination of the 
Metonic cycle of 19 years with the solar cycle of 28 years. His 
canon was published at Antwerp in 1633 or 1634, De doctrina tem- 
porum sive commentarius in Victorii Aquitani et aliorum canones 
pas c hales. 



360 A BUDGET OF PARADOXES. 

this cycle bears the name of Dionysius Exiguus, 12 a Scythian 
settled at Rome, about A. D. 530, who adapted it to his new 
yearly reckoning, when he abandoned the era of Diocletian 
as a commencement, and constructed that which is now in 
common use. 

4. With Dionysius, if not before, terminated all differ- 
ence as to the mode of keeping Easter which is of historical 
note: the increasing defects of the Easter Cycle produced 
in time the remonstrance of persons versed in astronomy, 
among whom may be mentioned Roger Bacon, 13 Sacro- 
bosco, 14 Cardinal Cusa, 15 Regiomontanus, 18 etc. From the 
middle of the sixth to that of the sixteenth century, one 
rule was observed. 

5. The mode of applying astronomy to chronology has 
always involved these two principles. First, the actual po- 
sition of the heavenly body is not the object of considera- 
tion, but what astronomers call its mean place, which may 
be described thus. Let a fictitious sun or moon move in 
the heavens, in such manner as to revolve among the fixed 
stars at an average rate, avoiding the alternate accelerations 
and retardations which take place in every planetary mo- 
tion. Thus the fictitious (say mean) sun and moon are 
always very near to the real sun and moon. The ordinary 
clocks show time by the mean, not the real, sun : and it was 
always laid down that Easter depends on the opposition 
(or full moon) of the mean sun and moon, not of the real 
ones. Thus we see that, were the Calendar ever so correct 

" He went to Rome about 497, and died there in 540. He wrote 
his Liber de paschate in 525, and it was in this work that the Chris- 
tian era was first used for calendar purposes. 

11 See note 6, page 126. 

"Johannes de Sacrobosco (Holy wood), or John of Holywood. 
The name was often written, without regard to its etymology, 
Sacrobusto. He was educated at Oxford and taught in Paris until 
his death (1256). He did much to make the Hindu-Arabic numer- 
als known to European scholars. 

11 See note 2, page 44. 
" See note 2, page 48. 



EASTER DAY PARADOXERS. 361 

as to the mean moon, it would be occasionally false as to the 
true one: if, for instance, the opposition of the mean sun 
and moon took place at one second before midnight, and that 
of the real bodies only two seconds afterwards, the calendar 
day of full moon would be one day before that of the com- 
mon almanacs. Here is a way in which the discussions of 
1818 and 1845 might have arisen: the British legislature has 
defined the moon as the regulator of the paschal calendar. 
But this was only a part of the mistake. 

6. Secondly, in the absence of perfectly accurate knowl- 
edge of the solar and lunar motion (and for convenience, 
even if such knowledge existed), cycles are, and always have 
been taken, which serve to represent those motions nearly. 
The famous Metonic cycle, which is introduced into eccle- 
siastical chronology under the name of the cycle of the 
golden numbers, is a period of 19 Julian 17 years. This 
period, in the old Calendar, was taken to contain exactly 
235 lunations, or intervals between new moons, of the mean 
moon. Now the state of the case is : 

19 average Julian years make 6939 days 18 hours. 

235 average lunations make 6939 days 16 hours 31 
minutes. 

So that successive cycles of golden numbers, supposing 
the first to start right, amount to making the new moons 
fall too late, gradually, so that the mean moon of this cycle 
gains 1 hour 29 minutes in 19 years upon the mean moon 
of the heavens, or about a day in 300 years. When the 
Calendar was reformed, the calendar new moons were four 
days in advance of the mean moon of the heavens : so that, 
for instance, calendar full moon on the 18th usually meant 
real full moon on the 14th. 

7. If the difference above had not existed, the moon of 
the heavens (the mean moon at least), would have returned 

"The Julian year is a year of the Julian Calendar, in which 
there is leap year every fourth year. Its average length is therefore 
365 days and a quarter. A. De M. 



362 A BUDGET OF PARADOXES. 

permanently to the same days of the month in 19 years ; 
with an occasional slip arising from the unequal distribu- 
tion of the leap years, of which a period contains sometimes 
five and sometimes four. As a general rule, the days of 
new and full moon in any one year would have been also 
the days of new and full moon of a year having 19 more 
units in its date. Again, if there had been no leap years, 
the days of the month would have returned to the same 
days of the week every seven years. The introduction of 
occasional 29ths of February disturbs this, and makes the 
permanent return of month days to week days occur only 
after 28 years. If all had been true, the lapse of 28 times 19, 
or 532 years, would have restored the year in every point: 
that is, A. D. 1, for instance, and A. D. 533, would have had 
the same almanac in every matter relating to week days, 
month days, sun, and moon (mean sun and moon at least). 
And on the supposition of its truth, the old system of Diony- 
sius was framed. Its errors, are, first, that the moments 
of mean new moon advance too much by 1 h. 29 m. in 19 
average Julian years; secondly, that the average Julian 
year of 365 J days is too long by llm. 10s. 

8. The Council of Trent, moved by the representations 
made on the state of the Calendar, referred the considera- 
tion of it to the Pope. In 1577, Gregory XIII 18 submitted 
to the Roman Catholic Princes and Universities a plan pre- 
sented to him by the representatives of Aloysius Lilius, 19 
then deceased. This plan being approved of, the Pope nomi- 
nated a commission to consider its details, the working mem- 
ber of which was the Jesuit Clavius. A short work was 
prepared by Clavius, descriptive of the new Calendar: this 

18 Ugo Buoncompagno (1502-1585) was elected pope in 1572. 

19 He was a Calabrian, and as early as 1552 was professor of 
medicine at Perugia. In 1576 his manuscript on the reform of the 
calendar was presented to the Roman Curia by his brother, An- 
tonius. The manuscript was not printed and it has not been pre- 
served. 



EASTER DAY PARADOXERS. 363 

was published 20 in 1582, with the Pope's bull (dated Febru- 
ary 24, 1581) prefixed. A larger work was prepared by 
Clavius, containing fuller explanation, and entitled Romani 
Calendarii a Gregorio XIII. Pontifice Maximo restituti Ex- 
plicatio. This was published at Rome in 1603, and again 
in the collection of the works of Clavius in 1612. 

9. The following extracts from Clavius settle the question 
of the meaning of the term moon, as used in the Calendar : 

"Who, except a few who think they are very sharp- 
sighted in this matter, is so blind as not to see that the 14th 
of the moon and the full moon are not the same things in 

the Church of God? Although the Church, in finding the 

new moon, and from it the 14th day, uses neither the true 
nor the mean motion of the moon, but measures only ac- 
cording to the order of a cycle, it is nevertheless undeniable 
that the mean full moons found from astronomical tables are 
of the greatest use in determining the cycle which is to be 

preferred the new moons of which cycle, in order to 

the due celebration of Easter, should be so arranged that 
the 14th days of those moons, reckoning from the day of 
new moon inclusive, should not fall two or more days before 
the mean full moon, but only one day, or else on the very 
day itself, or not long after. And even thus far the Church 
need not take very great pains .... for it is sufficient that all 
should reckon by the 14th day of the moon in the cycle, even 
though sometimes it should be more than one day before or 
after the mean full moon .... We have taken pains that in 
our cycle the new moons should follow the real new moons, 
so that the 14th of the moon should fall either the day be- 
fore the mean full moon, or on that day, or not long after ; 
and this was done on purpose, for if the new moon of the 
cycle fell on the same day as the mean new moon of the 

20 The title of this work, which is the authority on all points of 
the new Calendar, is Kalendarium Gregorianum Perpetuum. Cum 
Privilegio Summi Pontificis Et Aliorum Principum. Roma, Ex 
Officina Dominici Bascz. MDLXXXII. Cum Licentia Superiorum 
(quarto, pp. 60). A. De M. 



364 A BUDGET OF PARADOXES. 

astronomers, it might chance that we should celebrate Easter 
on the same day as the Jews or the Quartadeciman heretics, 
which would be absurd, or else before them, which would 
be still more absurd." 

From this it appears that Clavius continued the Calen- 
dar of his predecessors in the choice of the fourteenth day 
of the moon. Our legislature lays down the day of the full 
moon: and this mistake appears to be rather English than 
Protestant; for it occurs in missals published in the reign 
of Queen Mary. The calendar lunation being 29| days, 
the middle day is the fifteenth day, and this is and was 
reckoned as the day of the full moon. There is every 
right to presume that the original passover was a feast of 
the real full moon : but it is most probable that the moons 
were then reckoned, not from the astronomical conjunction 
with the sun, which nobody sees except at an eclipse, but 
from the day of -first visibility of the new moon. In fine 
climates this would be the day or two days after conjunction ; 
and the fourteenth day from that of first visibility inclusive, 
would very often be the day of full moon. The following 
is then the proper correction of the precept in the Act of 
Parliament : 

Easter Day, on which the rest depend, is always the 
First Sunday after the fourteenth day of the calendar moon 
which happens upon or next after the Twenty-first day of 
March, according to the rules laid down for the construction 
of the Calendar-, and if the fourteenth day happens upon a 
Sunday, Easter Day is the Sunday after. 

10. Further, it appears that Clavius valued the celebra- 
tion of the festival after the Jews, etc., more than astronom- 
ical correctness. He gives comparison tables which would 
startle a believer in the astronomical intention of his Calen- 
dar: they are to show that a calendar in which the moon is 
always made a day older than by him, represents the heavens 
better than he has done, or meant to do. But it must be 
observed that this diminution of the real moon's age has 



EASTER DAY PARADOXERS. 365 

a tendency to make the English explanation often practically 
accordant with the Calendar. For the fourteenth day of 
Clavius is generally the fifteenth day of the mean moon of 
the heavens, and therefore most often that of the real 
moon. But for this, 1818 and 1845 would not have been 
the only instances of our day in which the English precept 
would have contradicted the Calendar. 

11. In the construction of the Calendar, Clavius adopted 
the ancient cycle of 532 years, but, we may say, without 
ever allowing it to run out. At certain periods, a shift is 
made from one part of the cycle into another. This is done 
whenever what should be Julian leap year is made a com- 
mon year, as in 1700, 1800, 1900, 2100, etc. It is also done 
at certain times to correct the error of 1 h. 19 m., before 
referred to, in each cycle of golden numbers : Clavius, to 
meet his view of the amount of that error, put forward 
the moon's age a day 8 times in 2,500 years. As we cannot 
enter at full length into the explanation, we must content 
ourselves with giving a set of rules, independent of tables, 
by which the reader may find Easter for himself in any 
year, either by the old Calendar or the new. Any one who 
has much occasion to find Easters and movable feasts should 
procure Francceur's 21 tables. 

12. Rule for determining Easter Day of the Gregorian 
Calendar in any year of the new style. To the several parts 

* a Manueh-Roret. Theorie du Calendrier et collection de tous 

les Calendriers des Annees passees et futures Par L. B. Fran- 

cceur,. . .Paris, a la librairie encyclopedique de Roret, rue Haute- 
feuille, 10 bis. 1842. (i2mo.) In this valuable manual, the 35 
possible almanacs are given at length, with such preliminary tables 
as will enable any one to find, by mere inspection, which almanac 
he is to choose for any year, whether of old or new style. [1866. 
I may now refer to my own Book of Almanacs, for the same pur- 
pose]. A. De M. 

Louis Benjamin Francceur (1773-1849), after holding positions 
in the Ecole polytechnique (1804) and the Lycee Charlemagne 
(1805), became professor of higher algebra in the University of 
Paris (1809). His Cours complet des mathematiques pures was well 
received, and he also wrote on mechanics, astronomy, and geodesy. 



366 A BUDGET OF PARADOXES. 

of the rule are annexed, by way of example, the results for 
the year 1849. 

I. Add i to the given year. ( 1850) . 

II. Take the quotient of the given year divided by 4, neglecting 
the remainder. (462). 

III. Take 16 from the centurial figures of the given year, if it can 

be done, and take the remainder. (2). 

IV. Take the quotient of III. divided by 4, neglecting the re- 

mainder, (o). 

V. From the sum of L, II., and IV., subtract III. (2310). 
VI. Find the remainder of V. divided by 7. (o). 
VII. Subtract VI. from 7; this is the number of the dominical 

letter A B C D I F G (7 ; dominical letter G > 

VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the 
golden number. (7). 

IX. From the centurial figures of the year subtract 17, divide by 

25, and keep the quotient, (o). 

X. Subtract IX. and 15 from the centurial figures, divide by 3, 
and keep the quotient, (i). 

XL To VIII. add ten times the next less number, divide by 30, and 

keep the remainder. (7). 

XII. To XL add X. and IV., and take away III., throwing out 
thirties, if any. If this give 24, change it into 25. If 25, 
change it into 26, whenever the golden number is greater 
than ii. If o, change it into 30. Thus we have the epact, or 
age of the Calendar moon at the beginning of the year. (6). 

When the Epact is 23, or less. When the Epact is greater than 23. 



XIII. Subtract XII., the epact, 

from 45. (39). 

XIV. Subtract the epact from 

27, divide by 7, and 
keep the remainder, or 
7, if there be no re- 
mainder. (7). 



XIII. Subtract XII., the epact, 

from 75. 

XIV. Subtract the epact from 

57, divide by 7, and 
keep the remainder, or 
7, if there be no re- 
mainder. 



XV. To XIII. add VII., the dominical number, (and 7 besides, if 
XIV. be greater than VII.,) and subtract XIV., the result 
is the day of March, or if more than 31, subtract 31, and 



EASTER DAY PARADOXERS. 



367 



the result is the day of April, on which Easter Sunday 
falls. (39; Easter Day is April 8). 

In the following examples, the several results leading 
to the final conclusion are tabulated. 



GIVEN YEAR 


1592 


1637 


1723 


1853 


2018 


4686 


I. 


1593 


1638 


1724 


1854 


2019 


4687 


II. 


398 


409 


430 


463 


504 


1171 


III. 








1 


2 


4 


30 


IV. 














1 


7 


V. 


1991 


2047 


2153 


2315 


2520 


5835 


VI. 


3 


3 


4 


5 





4 


VII. 


4 


4 


3 


2 


7 


3 


VIII. 


16 


4 


14 


11 


5 


13 


IX. 

















1 


X. 











1 


1 


10 


XL 


16 


4 


24 


21 


15 


13 


XII. 


16 


4 


23 


20 


13 


say 30 


XIII. 


29 


41 


22 


25 


32 


45 


XIV. 


4 


2 


4 


7 


7 


6 


XV. 


29 


43 


28 


27 


32 


49 


Easter Day' 


Mar. 29 


Apr. 12 


Mar. 28 


Mar. 27 


Apr. 1 


Apr. 18 



13. Rule for determining Easter Day of the Antegrego- 
rian Calendar in any year of the old style. To the several 
parts of the rule are annexed, by way of example, the results 
for the year 1287. The steps are numbered to correspond 
with the steps of the Gregorian rule, so that it can be seen 
what augmentations the latter requires. 

I. Set down the given year. (1287). 
II. Take the quotient of the given year divided by 4, neglecting 

the remainder (321). 

V. Take 4 more than the sum of I. and II. (1612). 
VI. Find the remainder of V. divided by 7. (2). 
VII. Subtract VI. from 7; this is the number of the dominical 



letter 



ABCDEFG 



(5; dominical letter E). 



1234567. 

VIII. Divide one more than the given year by 19, the remainder 

(or 19 if no remainder) is the golden number. (15). 
XII. Divide 3 less than n times VIII. by 30; the remainder (or 30 
if there be no remainder) is the epact (12). 



368 A BUDGET OF PARADOXES. 



When the Epact is 23, or less. When the Epact is greater than 23. 



XIII. Subtract XII., the epact, 

from 45. (33). 

XIV. Subtract the epact from 

27, divide by 7, and 
keep the remainder, or 
7, if there be no re- 
mainder, (i). 



XIII. Subtract XII., the epact, 

from 75. 

XIV. Subtract the epact from 

57, divide by 7, and 
keep the remainder, or 
7, if there be no re- 
mainder. 



XV. To XIII. add VII., the dominical number, (and 7 besides if 
XIV. be greater than VII.,) and subtract XIV., the result 
is the day of March, or if more than 31, subtract 31, and the 
result is the day of April, on which Easter Sunday (old 
style) falls. (37; Easter Day is April 6). 

These rules completely represent the old and new Cal- 
endars, so far as Easter is concerned. For further explana- 
tion we must refer to the articles cited at the commence- 
ment. 

The annexed is the table of new and full moons of the 
Gregorian Calendar, cleared of the errors made for the 
purpose of preventing Easter from coinciding with the 
Jewish Passover. 

The second table (page 370) contains e pacts, or ages of 
the moon at the beginning of the year: thus in 1913, the 
epact is 22, in 1868 it is 6. This table goes from 1850 to 
1999: should the New Zealander not have arrived by that 
time, and should the churches of England and Rome then 
survive, the epact table may be continued from their liturgy- 
books. The way of using the table is as follows : Take the 
epact of the required year, and find it in the first or last 
column of the first table, in line with it are seen the calendar 
days of new and full moon. Thus, when the epact is 17, 
the new and full moons of March fall on the 13th and 28th. 
The result is, for the most part, correct: but in a minority 
of cases there is an error of a day. When this happens, the 
error is almost always a fraction of a day much less than 
twelve hours. Thus, when the table gives full moon on the 
27th, and the real truth is the 28th, we may be sure it is early 





Jan. 


Feb. 


Mar 


Apr. 


May 


June 


July 


Aug 


Sep. 


Oct. 


Nov 


Dec. 




1 \ 


ag 
14 


27 
13 


29 
M 


27 
13 


27 

12 


25 
ii 


25 

IO 


23 
9 


22 

7 


21 

7 


20 
5 


19 
5 


i 1 


2 { 


28 
13 


26 

12 


28 
U 


26 

13 


26 
ii 


24 

IO 


24 
9 


32 

8 


31 

6 


20 

6 


19 

4 


18 

4 


f 2 


3 


37 
12 


25 
II 


27 

12 


25 
ii 


25 

10 


23 
9 


3 


21 

7 


20 

5 


19 

5 


18 
3 


17 
3 


1 3 


4 


26 
ii 


24 
IO 


26 
II 


24 

IO 


24 

9 


22 
8 


22 

7 


20 
6 


19 

4 


18 

4 


17 

a 


16 

2,31 


El 


5 ; 


25 

10 


23 

9 


25 
IO 


23 

9 


'i 


21 

7 


21 

6 


19 
5 


18 
3 


17 
3 


16 

i 


15 
1,30 


1 ^ 


6 { 


24 
9 


22 
8 


24 

9 


22 
8 


22 

7 


20 
6 


20 

5 


18 

4 


17 

a 


16 
2,31 


15 
30 


14 
29 


1 ^ 


7 { 


23 


21 

7 


1 


21 

7 


21 

6 


19 
5 


19 

4 


17 
3 


16 


15 
i,3 


14 
29 


Ii 


f 7 


8 | 


22 
7 


20 

6 


22 

7 


20 

6 


20 

5 


18 

4 


18 
3 


16 
2,31 


15 
3 


14 
29 


3 


12 

27 


8 


9 


21 

6 


19 

5 


21 

6 


19 

5 


19 

4 


17 
3 


17 

a 


15 
1,30 


14 
29 


X 


12 
27 


II 
26 


9 


10 j 


20 

5 


18 

4 


20 
5 


18 

4 


18 
3 


16 

2 


16 
i.3i 


14 
29 


U 


12 

27j 


II 
26 


10 
25 


10 


11] 


i9 

4 


17 
3 


19 
4 


17 
3 


17 

2 


IS 
1,30 


15 
30 


Ji 


12 
27 


II 

26 


IO 

25 


9 

24 


1 H 


12 { 


18 
3 


16 

2 


18 
3 


16 

2 


16 
i,3i 


14 
29 


14 
29 


12 
27 


II 
26 


10 

25 


9 
24 


8 
23 


i 12 


13 | 


17 

2 


15 


17 

2 


IS 

1,30 


IS 
30 


11 


11 


ii 
26 


IO 
25 


9 

24 


8 
23 


7 

22 


f 13 


14 j 


16 
1.3* 


14 


16 
i3i 


14 
29 


14 
29 


12 
27 


12 
27 


IO 

25 


9 
24 


8 
23 


7 

22 


6 

21 


i i 4 


15 { 


I I5 
1 3 


3 


15 

30 


Ii 


Ii 


II 
26 


II 
26 


9 

24 


8 
23 


7 
22 


6 

21 


5 

20 


1 I 5 


16 | 


14 
29 


12 
27 


14 
29 


12 
27 


12 
27 


IO 
25 


IO 
25 


8 
23 


7 

22 


6 

21 


5 
20 


4 
19 


i 16 


17 | 


ij 


II 
26 


ii 


II 
26 


II 
26 


9 
24 


9 

24 


7 

22 


6 

21 


5 
20 


4 
19 


,1 


{ 17 


18 j 


12 

27 


IO 
25 


12 
27 


IO 
25 


IO 
25 


8 
23 


8 
23 


6 

21 


5 

20 


4 
19 


,1 


2 
17 


18 


191 


II 
26 


9 

24 


II 
26 


9 

24 


9 

24 


7 

22 


7 

22 


5 

20 


4 
19 


18 


2 
17 


'A' 


19 


20 { 


IO 
25 


8 
23 


10 
25 


8 
23 




6 
21 


6 

21 


4 
19 


,i 


2 
17 


'A 1 


30 

is 


20 


21 


9 
24 


7 

22 


9 
24 


7 

22 


7 

22 


5 

20 


5 

20 


j 


2 
17 


'ft 1 


29 
15 


29 
14 


21 


22 


8 
23 


6 

21 


8 
23 


6 

21 


6 

21 


4 
19 


4 
19 


2 
17 


1,30 

16 


30 

u 


28 
14 


28 

13 


f 22 


23 


7 

22 


5 

20 


7 

22 


5 

20 


5 
20 


ii 


18 


1,31 

16 


29 

15 


29 

- 14 .- 


27 
13 


27 

12 


23 


24 j 


6 
21 


19 


21 


19 


19 


17 


17 


1,30 
'5 


29 

'4 


28 
*3 


27 

12 


26 
II 


} 24 


25 


S 

20 


4 
19 


5 
20 


4 
19 


j 


2 
17 


'$ 


29 
15 


28 
13 


27 
13 


26 
II 


25 
II 


25 


26 i 


4 
19 


,| 


4 
19 


j 


2 
17 


1,30 

16 


30 
15 


28 
14 


27 

12 


26 

12 


25 
IO 


24 
IO 


} 26 


27 | 


,1 


2 
17 


,1 


2 

17 


H 1 

16 


29 

15 


29 
14 


27 
13 


26 
II 


25 
II 


24 

9 


23 

9 


27 


28 j 


2 
*7 


I 

16 


2 
17 


i,3p 
16 


30 
15 


28 
14 


28 
13 


26 

12 


25 
IO 


24 
IO 


2 i 


22 

8 


28 


29 j 


1,3,1 

16 


15 


1,31 

16 


29 
15 


29 
14 


27 
13 


27 

12 


25 
II 


24 

9 


23 

9 


22 

7 


21 

7 


29 


30 j 


30 

15 


28 
14 


30 

u 


28 
14 


28 
13 


26 

12 


26 
II 


24 
10 


2 i 


22 
8 


21 

6 


20 
6 


30 




Jan. 


Feb. 


Mar. 


Apr. 


May 


'une 


Tuly 


Aug. 


Sep. 


Oct. 


Nov. 


Dec. 





370 



A BUDGET OF PARADOXES. 








1 


2 


3 


4 


5 


6 


7 


8 


g 


185 


17 


28 


19 


20 


2 


12 


23 


4 


15 


26 


186 


7 


18 


30 


11 


22 


3 


14 


25 


6 


17 


187 


28 


9 


20 


1 


12 


23 


4 


15 


26 


7 


188 


18 


30 


11 


22 


3 


14 


25 


6 


17 


28 


189 


9 


21 


1 


12 


23 


4 


15 


26 


7 


18 


190 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


191 


19 


30 


11 


22 


3 


14 


26 


6 


17 


29 


192 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 


193 


30 


11 


22 


3 


14 


26 


6 


17 


29 


10 


194 


21 


2 


13 


24 


5 


16 


27 


8 


19 


30 


195 


11 


22 


3 


14 


26 


6 


17 


29 


10 


21 


196 


2 


13 


24 


5 


16 


27 


8 


19 


30 


11 


197 


22 


3 


14 


26 


6 


17 


29 


10 


21 


2 


198 


13 


24 


5 


16 


27 


8 


19 


30 


11 


22 


199 


3 


14 


26 


6 


17 


29 


10 


21 


2 


13 



on the 28th. For example, the year 1867. The epact is 25, 
and we find in the table: 

J. F. M. AP. M. JU. JL. AU. S. O. N. D. 

New .... 5+ 4 5+4 3+2 1,31 29 28- 27 26 25 
Full .... 20 19- 20 19- 18 17 16 15 13- 13 11+ 11 

When the truth is the day after + is written after the 
date; when the day before, . Thus, the new moon of 
March is on the 6th ; the full moon of April is on the 18th. 



EASTER DAY PARADOXERS. 371 

I now introduce a small paradox of my own; and as I 
am not able to prove it, I am compelled to declare that 
any one who shall dissent must be either very foolish or 
very dishonest, and will make me quite uncomfortable about 
the state of his soul. This being settled once for all, I pro- 
ceed to say that the necessity of arriving at the truth about 
the assertions that the Nicene Council laid down astronom- 
ical tests led me to look at Fathers, Church histories, etc. 
to an extent which I never dreamed of before. One con- 
clusion which I arrived at was, that the Nicene Fathers had 
a knack of sticking to the question which many later councils 
could not acquire. In our own day, it is not permitted 
to Convocation seriously to discuss any one of the points 
which are bearing so hard upon their resources of defence 
the cursing clauses of the Athanasian Creed, for example. 
And it may be collected that the prohibition arises partly 
from fear that there is no saying where a beginning, if 
allowed, would end. There seems to be a suspicion that 
debate, once let loose, would play up old Trent with the 
liturgy, and bring the whole book to book. But if any one 
will examine the real Nicene Creed, without the augmen- 
tation, he will admire the way in which the framers stuck 
to the point, and settled what they had to decide, according to 
their view of it. With such a presumption of good sense 
in their favor, it becomes easier to believe in any claim which 
may be made on their behalf to tact or sagacity in settling 
any other matter. And I strongly suspect such a claim may 
be made for them on the Easter question. 

I collect from many little indications, both before and 
after the Council, that the division of the Christian world 
into Judaical and Gentile, though not giving rise to a sec- 
tarian distinction expressed by names, was of far greater 
force and meaning than historians prominently admit. I 
took note of many indications of this, but not notes, as it was 
not to my purpose. If it were so, we must admire the dis- 
cretion of the Council. The Easter question was the fight- 



372 A BUDGET OF PARADOXES. 

ing ground of the struggle: the Eastern or Judaical Chris- 
tians, with some varieties of usage and meaning, would 
have the Passover itself to be the great feast, but taken in 
a Christian sense; the Western or Gentile Christians, would 
have the commemoration of the Resurrection, connected 
with the Passover only by chronology. To shift the Passover 
in time, under its name, Pascha, without allusion to any of 
the force of the change, was gently cutting away the ground 
from under the feet of the Conservatives. And it was done 
in a very quiet way: no allusion to the precise character of 
the change ; no hint that the question was about two different 
festivals: "all the brethren in the East, who formerly cele- 
brated this festival at the same time as the Jews, will in fu- 
ture conform to the Romans and to us." The Judaizers 
meant to be keeping the Passover as a Christian feast : they 
are gently assumed to be keeping, not the Passover, but a 
Christian feast; and a doctrinal decision is quietly, but effi- 
ciently, announced under the form of a chronological ordi- 
nance. Had the Council issued theses of doctrine, and ex- 
communicated all dissentients, the rupture of the East and 
West would have taken place earlier by centuries than it did. 
The only place in which I ever saw any part of my paradox 
advanced, was in an article in the Examiner newspaper, 
towards the end of 1866, after the above was written. 

A story about Christopher Clavius, the workman of the 
new Calendar. I chanced to pick up "Albertus Pighius 
Campensis de sequinoctiorum solsticiorumque inventione . . . 
Ejusdem de ratione Paschalis celebrationis, De que Restitu- 
tione ecclesiastici Kalendarii," Paris, 1520, folio. 22 On the 
title-page were decayed words followed by ". .hristophor. . 
C. .ii, 1556 (or 8)," the last blank not entirely erased by 
time, but showing the lower halves of an / and of an a, and 

M Albertus Pighius, or Albert Pigghe, was born at Kempen c. 
1490 and died at Utrecht in 1542. He was a mathematician and a 
firm defender of the faith, asserting the supremacy of the Pope and 
attacking both Luther and Calvin. He spent some time in Rome. 
His greatest work was his Hierarchic? ecclesiastics assertio (1538). 



A COUPLE OF MINOR PARADOXES. 373 

rather too much room for a v. It looked very like E Libris 
Christophori Clavii 1556. By the courtesy of some members 
of the Jesuit body in London, I procured a tracing of the 
signature of Clavius from Rome, and the shapes of the 
letters, and the modes of junction and disjunction, put the 
matter beyond question. Even the extra space was ex- 
plained ; he wrote himself Clawius. Now in 1556, Clavius 
was nineteen years old : it thus appears probable that the 
framer of the Gregorian Calendar was selected, not merely 
as a learned astronomer, but as one who had attended to the 
calendar, and to works on its reformation, from early youth. 
When on the subject I found reason to think that Clavius 
had really read this work, and taken from it a phrase or two 
and a notion or two. Observe the advantage of writing the 
baptismal name at full length. 

A COUPLE OF MINOR PARADOXES. 

The discovery of a general resolution of all superior finite equa- 
tions, of every numerical both algebraick and transcendent 
form. By A. P. Vogel, 1 mathematician at Leipzick. Leipzick 
and London, 1845, 8vo. 

This work is written in the English of a German who 
has not mastered the idiom: but it is always intelligible. It 
professes to solve equations of every degree "in a more ex- 
tent sense, and till to every degree of exactness." The gen- 
eral solution of equations of all degrees is a vexed question, 
which cannot have the mysterious interest of the circle prob- 
lem, and is of a comparatively modern date. 2 Mr. Vogel 

1 This was A. F. yogel. The work was his translation from 
the German edition which appeared at Leipsic the same year, Ent- 
deckung einer numerischen General-Auflosung aller hoheren end- 
lichen Gleichungen von jeder beliebigen algebraischen und transcen- 
denten Form. 

"The latest edition of Burnside and Panton's Theory of Equa- 
tions has this brief summary of the present status of the problem: 
"Demonstrations have been given by Abel and Wantzel (see Serret's 
Cours d'Algebre Superieure, Art 516)^ of the impossibility of re- 
solving algebraically equations unrestricted in form, of a degree 
higher than the fourth. A transcendental solution, however, of the 



374 A BUDGET OF PARADOXES. 

announces a forthcoming treatise in which are resolved the 
"last impossibilities of pure mathematics." 

Elective Polarity the Universal Agent. By Frances Barbara 
Burton, authoress of 'Astronomy familiarized/ 'Physical As- 
tronomy/ &c. London, 1845, 8vo. 3 

The title gives a notion of the theory. The first sentence 
states, that 12,500 years ago a Lyrae was the pole-star, and 
attributes the immense magnitude of the now fossil animals 
to a star of such "polaric intensity as Vega pouring its 
magnetic streams through our planet." Miss Burton was 
a lady of property, and of very respectable acquirements, 
especially in Hebrew; she was eccentric in all things. 

1867. Miss Burton is revived by the writer of a book 
on meteorology which makes use of the planets : she is one 
of his leading minds. 4 

SPECULATIVE THOUGHT IN ENGLAND. 

In the year 1845 the old Mathematical Society was 
merged in the Astronomical Society. The circle-squarers, 
etc., thrive more in England than in any other country: 
there are most weeds where there is the largest crop. Specu- 
lation, though not encouraged by our Government so much 
as by those of the Continent, has had, not indeed such 
forcing, but much wider diffusion: few tanks, but many 
rivulets. On this point I quote from the preface to the 
reprint of the work of Ramchundra, 1 which I superintended 
for the late Court of Directors of the East India Company. 

quintic has been given by M. Hermite, in a form involving elliptic 
integrals." 

* There was a second edition of this work in 1846. The author's 
Astronomy Simplified was published in 1838, and the Thoughts on 
Physical Astronomy in 1840, with a second edition in 1842. 

*This was The Science of the Weather, by several authors 

edited by B., Glasgow, 1867. 

1 This was Y. Ramachandra, son of Sundara Lala. He was a 
teacher of science in Delhi College, and the work to which De 
Morgan refers is A Treatise on problems of Maxima and Minima 
solved by Algebra, which appeared at Calcutta in 1850. De Morgan's 
edition was published at London nine years later. 



SPECULATIVE THOUGHT IN ENGLAND. 375 

"That sound judgment which gives men well to know 
what is best for them, as well as that faculty of invention 
which leads to development of resources and to the increase 
of wealth and comfort, are both materially advanced, per- 
haps cannot rapidly be advanced without, a great taste for 
pure speculation among the general mass of the people, 
down to the lowest of those who can read and write. Eng- 
land is a marked example. Many persons will be surprised 
at this assertion. They imagine that our country is the 
great instance of the refusal of all unpractical knowledge in 
favor of what is useful. I affirm, on the contrary, that there 
is no country in Europe in which there has been so wide 
a diffusion of speculation, theory, or what other unpractical 
word the reader pleases. In our country, the scientific so- 
ciety is always formed and maintained by the people; in 
every other, the scientific academy most aptly named 
has been the creation of the government, of which it has 
never ceased to be the nursling. In all the parts of England 
in which manufacturing pursuits have given the artisan 
some command of time, the cultivation of mathematics and 
other speculative studies has been, as is well known, a very 
frequent occupation. In no other country has the weaver 
at his loom bent over the Principia of Newton ; in no other 
country has the man of weekly wages maintained his own 
scientific periodical. With us, since the beginning of the 
last century, scores upon scores perhaps hundreds, for I 
am far from knowing all of annuals have run, some their 
ten years, some their half-century, some their century and 
a half, containing questions to be answered, from which 
many of our examiners in the universities have culled mate- 
rials for the academical contests. And these questions have 
always been answered, and in cases without number by the 
lower order of purchasers, the mechanics, the weavers, and 
the printers' workmen. I cannot here digress to point out 
the manner in which the concentration of manufactures, 
and the general diffusion of education, have affected the 



376 A BUDGET OF PARADOXES. 

state of things ; I speak of the time during which the present 
system took its rise, and of the circumstances under which 
many of its most effective promoters were trained. In all 
this there is nothing which stands out, like the state-nour- 
ished academy, with its few great names and brilliant single 
achievements. This country has differed from all others in 
the wide diffusion of the disposition to speculate, which 
disposition has found its place among the ordinary habits 
of life, moderate in its action, healthy in its amount." 

THE OLD MATHEMATICAL SOCIETY. 

Among the most remarkable proofs of the diffusion of 
speculation was the Mathematical Society, which flourished 
from 1717 to 1845. Its habitat was Spitalfields, and I think 
most of its existence was passed in Crispin Street. It was 
originally a plain society, belonging to the studious artisan. 
The members met for discussion once a week ; and I believe 
I am correct in saying that each man had his pipe, his pot, 
and his problem. One of their old rules was that, "If any 
member shall so far forget himself and the respect due to 
the Society as in the warmth of debate to threaten or offer 
personal violence to any other member, he shall be liable to 
immediate expulsion, or to pay such fine as the majority of 
the members present shall decide." But their great rule, 
printed large on the back of the title page of their last book 
of regulations, was "By the constitution of the Society, it 
is the duty of every member, if he be asked any mathematical 
or philosophical question by another member, to instruct 
him in the plainest and easiest manner he is able." We shall 
presently see that, in old time, the rule had a more homely 
form. 

I have been told that De Moivre 1 was a member of this 

1 Abraham de Moivre (1667-1754), French refugee in London, 
poor, studying under difficulties, was a man with tastes in some re- 
spects like those of De Morgan. For one thing, he was a lover of 
books, and he had a good deal of interest in the theory of probabili- 
ties to which De Morgan also gave much thought. His introduction 



THE OLD MATHEMATICAL SOCIETY. 377 

Society. This I cannot verify: circumstances render it un- 
likely ; even though the French refugees clustered in Spital- 
fields; many of them were of the Society, which there is 
some reason to think was founded by them. But Dolland, 2 
Thomas Simpson, 3 Saunderson, 4 Crossley, 5 and others of 
known name, were certainly members. The Society grad- 
ually declined, and in 1845 was reduced to nineteen mem- 
bers. An arrangement was made by which sixteen of these 
members, who where not already in the Astronomical Society 
became Fellows without contribution, all the books and other 
property of the old Society being transferred to the new one. 
I was one of the committee which made the preliminary 
inquiries, and the reason of the decline was soon manifest. 
The only question which could arise was whether the mem- 
bers of the society of working men for this repute still 
continued were of that class of educated men who could 
associate with the Fellows of the Astronomical Society on 
terms agreeable to all parties. We found that the artisan 
element had been extinct for many years; there was not a 
man but might, as to education, manners, and position, have 
become a Fellow in the usual way. The fact was that life 
in Spitalfields had become harder: and the weaver could 

of imaginary quantities into trigonometry was an event of importance 
in the history of mathematics, and the theorem that bears his name, 
(cos0 + tsin0) = cosM0 + ismn<t>, is one of the most important 
ones in all analysis. 

"John Dolland (1706-1761), the silk weaver who became the 
greatest maker of optical instruments in his time. 

Thomas Simpson (1710-1761), also a weaver, taking his leisure 
from his loom at Spitalfields to teach mathematics. His New Treat- 
ise on Fluxions (1737) was written only two years after he began 
working in London, and six years later he was appointed professor 
of mathematics at Woolwich. He wrote many works on mathe- 
matics and Simpson's Formulas for computing trigonometric tables 
are still given in the text-books. 

4 Nicholas Saunderson (1682-1739), the blind mathematician. He 
lost his eyesight through smallpox ^when only a year old. At the age 
of 25 he began lecturing at Cambridge on the principles of the New- 
tonian philosophy. His Algebra, in two large volumes, was long the 
standard treatise on the subject. 

5 He was not in the class with the others mentioned. 



378 A BUDGET OF PARADOXES. 

only live from hand to mouth, and not up to the brain. The 
material of the old Society no longer existed. 

In 1798, experimental lectures were given, a small charge 
for admission being taken at the door : by this hangs a tale 
and a song. Many years ago, I found among papers of a 
deceased friend, who certainly never had anything to do 
with the Society, and who passed all his life far from Lon- 
don, a song, headed "Song sung by the Mathematical So- 
ciety in London, at a dinner given Mr. Fletcher, 8 a solicitor, 
who had defended the Society gratis/' Mr. Williams, 7 the 
Assistant Secretary of the Astronomical Society, formerly 
Secretary of the Mathematical Society, remembered that the 
Society had had a solicitor named Fletcher among the mem- 
bers. Some years elapsed before it struck me that my old 
friend Benjamin Gompertz, 8 who had long been a member, 
might have some recollection of the matter. The following 
is an extract of a letter from him (July 9, 1861) : 

"As to the Mathematical Society, of which I was a mem- 
ber when only 18 years of age, [Mr. G. was born in 1779], 
having been, contrary to the rules, elected under the age of 
21. How I came to be a member of that Society and con- 
tinued so until it joined the Astronomical Society, and was 
then the President was : I happened to pass a bookseller's 
small shop, of second-hand books, kept by a poor taylor, 
but a good mathematician, John Griffiths. I was very 
pleased to meet a mathematician, and I asked him if he would 
give me some lessons ; and his reply was that I was more 
capable to teach him, but he belonged to a society of mathe- 
maticians, and he would introduce me. I accepted the offer, 
and I was elected, and had many scholars then to teach, as 

a Not known in the literature of mathematics. 

7 Probably J. Butler Williams whose Practical Geodesy appeared 
in 1842, with a third edition in 1855. 

"Benjamin Gompertz (1779-1865) was debarred as a Jew from 
a university education. He studied mathematics privately and be- 
came president of the Mathematical Society. De Morgan knew him 
professionally through the fact that he was prominent in actuarial 
work. 



THE OLD MATHEMATICAL SOCIETY. 379 

one of the rules was, if a member asked for information, 
and applied to any one who could give it, he was obliged to 
give it, or fine one penny. Though I might say much with 
respect to the Society which would be interesting, I will for 
the present reply only to your question. I well knew Mr. 
Fletcher, who was a very clever and very scientific person. 
He did, as solicitor, defend an action brought by an informer 
against the Society I think for 5,000/. for giving lectures 
to the public in philosophical subjects [i. e., for unlicensed 
public exhibition with money taken at the doors]. I think 
the price for admission was one shilling, and we used to 
have, if I rightly recollect, from two to three hundred visi- 
tors. Mr. Fletcher was successful in his defence, and we got 
out of our trouble. There was a collection made to reward 
his services, but he did not accept of any reward: and I 
think we gave him a dinner, as you state, and enjoyed 
ourselves ; no doubt with astronomical songs and other 
songs; but my recollection does not enable me to say if 
the astronomical song was a drinking song. I think the 
anxiety caused by that action was the cause of some of the 
members' death. [They had, no doubt, broken the law in 
ignorance ; and by the sum named, the informer must have 
been present, and sued for a penalty on every shilling he 
could prove to have been taken]/' 

I by no means guarantee that the whole song I proceed 
to give is what was sung at the dinner: I suspect, by the 
completeness of the chain, that augmentations have been 
made. My deceased friend was just the man to add some 
verses, or the addition may have been made before it came 
into his hands, or since his decease, for the scraps contain- 
ing the verses passed through several hands before they 
came into mine. We may, however, be pretty sure that the 
original is substantially contained in what is given, and 
that the character is therefore preserved. I have had my- 
self to repair damages every now and then, in the way of 
conjectural restoration of defects caused by ill-usage. 



380 A BUDGET OF PARADOXES. 



THE ASTRONOMER'S DRINKING SONG. 

"Whoe'er would search the starry sky, 

Its secrets to divine, sir, 
Should take his glass I mean, should try 

A glass or two of wine, sir ! 
True virtue lies in golden mean, 

And man must wet his clay, sir; 
Join these two maxims, and 'tis seen 

He should drink his bottle a day, sir ! 

"Old Archimedes, reverend sage! 

By trump of fame renowned, sir, 
Deep problems solved in every page, 

And the sphere's curved surface found, 1 sir : 
Himself he would have far outshone, 

And borne a wider sway, sir, 
Had he our modern secret known, 

And drank a bottle a day, sir ! 

"When Ptolemy, 2 now long ago, 

Believed the earth stood still, sir, 
He never would have blundered so, 

Had he but drunk his fill, sir : 
He'd then have felt 3 it circulate, 

And would have learnt to say, sir, 
The true way to investigate 

Is to drink your bottle a day, sir ! 

"Copernicus, 4 that learned wight, 

The glory of his nation, 
With draughts of wine refreshed his sight, 
And saw the earth's rotation; 

1 Referring to the contributions of Archimedes (287-212 B.C.) 
to the mensuration of the sphere. 

*The famous Alexandrian astronomer (c. 87 c. 165 A. D.), 
author of the Almagest, a treatise founded on the works of Hip- 
parchus. 

"Dr. Whewell, when I communicated this song to him, started 
the opinion, which I had before him, that this was a very good idea, 
of which too little was made. A. De M. 

* See note 3, page 76. 



THE ASTRONOMER'S DRINKING SONG. 381 

Each planet then its orb described, 

The moon got under way, sir; 
These truths from nature he imbibed 

For he drank his bottle a day, sir ! 

"The noble 5 Tycho placed the stars, 

Each in its due location; 
He lost his nose 6 by spite of Mars, 

But that was no privation : 
Had he but lost his mouth, I grant 

He would have felt dismay, sir, 
Bless you ! he knew what he should want 

To drink his bottle a day, sir ! 

"Cold water makes no lucky hits ; 

On mysteries the head runs : 
Small drink let Kepler 7 time his wits 

On the regular polyhedrons : 
He took to wine, and it changed the chime, 

His genius swept away, sir, 
Through area varying 8 as the time 

At the rate of a bottle a day, sir ! 

"Poor Galileo, 8 forced to rat 

Before the Inquisition, 
E pur si muove 10 was the pat 
He gave them in addition : 

e The common epithet of rank : nobilis Tycho, as he was a noble- 
man. The writer had been at history. A. De M. 
See note 3, page 76. 

* He lost it in a duel, with Manderupius Pasbergius. A contem- 
porary, T. B. Laurus, insinuates that they fought to settle which was 
the best mathematician ! This seems odd, but it must be remembered 
they fought in the dark, "in tenebris densis" ; and it is a nice problem 
to shave off a nose in the dark, without any other harm. A. De M. 

Was this T. B. Laurus Joannes Baptista Laurus or Giovanni 
Battista Lauro (1581-1621), the poet and writer? 

T See note 3, page 76. 

* Referring to Kepler's celebrated law of planetary motion. He 
had previously wasted his time on analogies between the planetary 
orbits and the polyhedrons. A. De M. 

9 See note 3, page 76. 

10 "It does move though." 



382 A BUDGET OF PARADOXES. 

He meant, whate'er you think you prove, 

The earth must go its way, sirs ; 
Spite of your teeth I'll make it move, 

For I'll drink my bottle a day, sirs! 

"Great Newton, who was never beat 

Whatever fools may think, sir; 
Though sometimes he forgot to eat, 

He never forgot to drink, sir: 
Descartes 11 took nought but lemonade, 

To conquer him was play, sir; 
The first advance that Newton made 

Was to drink his bottle a day, sirl 

"D'Alembert, 12 Euler, 18 and Clairaut, 14 

Though they increased our store, sir, 
Much further had been seen to go 

Had they tippled a little more, sir ! 
Lagrange 15 gets mellow with Laplace, 16 

And both are wont to say, sir, 
The philosophe who's not an ass 

Will drink his bottle a day, sir ! 

"Astronomers ! what can avail 

Those who calumniate us ; 
Experiment can never fail 

With such an apparatus : 
Let him who'd have his merits known 

Remember what I say, sir; 
Fair science shines on him alone 

Who drinks his bottle a day, sir ! 

11 As great a lie as ever was told: but in 1800 a compliment to 
Newton without a fling at Descartes would have been held a lopsided 
structure. A. De M. 

" Jean-le-Rond D'Alembert (1717-1783), the foundling who was 
left on the steps of Jean-le-Rond in Paris, and who became one of 
the greatest mathematical physicists and astronomers of his century. 

"Leonhard Euler (1707-1783), friend of the Bernoullis, the 
greatest of Swiss mathematicians, prominent in the theory of num- 
bers, and known for discoveries in all lines of mathematics as then 
studied. 

14 See notes 2, 3, page 219. 

15 See note 3, page 288. 
la See note 6, page 255. 



LE VERRIER'S PLANET. 383 

"How light we reck of those who mock 

By this we'll make to appear, sir, 
We'll dine by the sidereal 17 clock 

For one more bottle a year, sir : 
But choose which pendulum you will, 

You'll never make your way, sir, 
Unless you drink and drink your fill, 

At least a bottle a day, sir !" 

Old times are changed, old manners gone! 

There is a new Mathematical Society, 18 and I am, at this 
present writing (1866), its first President. We are very 
high in the newest developments, and bid fair to take a place 
among the scientific establishments. Benjamin Gompertz, 
who was President of the old Society when it expired, was 
the link betw r een the old and new body: he was a member 
of ours at his death. But not a drop of liquor is seen at our 
meetings, except a decanter of water : all our heavy is a fer- 
mentation of symbols ; and we do not draw it mild. There 
is no penny fine for reticence or occult science ; and as to a 
song! not the ghost of a chance. 

1826. The time may have come when the original docu- 
ments connected with the discovery of Neptune may be 
worth revising. The following are extracts from the 
Athenaum of October 3 and October 17: 

LE VERRIER'S 1 PLANET. 

We have received, at the last moment before making up 
for press, the following letter from Sir John Herschel, 2 

"The siderial day is about four minutes short of the solar; 
there are 366 sidereal days in the year. A. De M. 

18 The founding of the London Mathematical Society is dis- 
cussed by Mrs. De Morgan in her Memoir (p. 281). The idea came 
from a conversation between her brilliant son, George Campbell De 
Morgan, and his friend Arthur Cowper Ranyard in 1864. The meet- 
ing of organization was held on Nov. 7, 1864, with Professor De 
Morgan in the chair, and the first regular meeting on January 16, 
1865. 

1 See note 8, page 43. 

2 See note 5, page 80. 



384 A BUDGET OF PARADOXES. 

in reference to the matter referred to in the communication 
from Mr. Hind 3 given below: 

"Collingwood, Oct. 1. 

"In my address to the British Association assembled at 
Southampton, on the occasion of my resigning the chair to 
Sir R. Murchison, 4 I stated, among the remarkable astro- 
nomical events of the last twelvemonth, that it had added a 
new planet to our list, adding, 'it has done more, it has 
given us the probable prospect of the discovery of another. 
We see it as Columbus saw America from the shores of 
Spain. Its movements have been felt, trembling along the 
far-reaching line of our analysis, with a certainty hardly 
inferior to that of ocular demonstration/ These expres- 
sions are not reported in any of the papers which profess 
to give an account of the proceedings, but I appeal to all 
present whether they were not used. 

"Give me leave to state my reasons for this confidence ; 
and, in so doing, to call attention to some facts which de- 
serve to be put on record in the history of this noble dis- 
covery. On July 12, 1842, the late illustrious astronomer, 
Bessel, 5 honored me with a visit at my present residence. 
On the evening of that day, conversing on the great work 
of the planetary reductions undertaken by the Astronomer 
Royal 6 then in progress, and since published, 7 M. Bessel 
remarked that the motions of Uranus, as he had satisfied 

'John Russell Hind (b. 1823), the astronomer. Between 1847 
and 1854 he discovered ten planetoids. 

4 Sir Roderick Impey Murchison (1792-1871), the great geolo- 
gist. He was knighted in 1846 and devoted the latter part of his 
life to the work of the Royal Geographical Society and to the geol- 
ogy of Scotland. 

6 Friedrich Wilhelm Bessel (1784-1846), the astronomer and 
physicist. He was professor of astronomy at Konigsberg. 

6 This was the Reduction of the Observations of Planets made 
.... from 1750 to 1830: computed. .. .under the superintendence of 
George Biddell Airy (1848). See note 2, page 85. 

T The expense of this magnificent work was defrayed by Govern- 
ment grants, obtained, at the instance of the British Association, in 
1833. A. De M. 



LE VERRIER'S PLANET. 385 

himself by careful examination of the recorded observations, 
could not be accounted for by the perturbations of the known 
planets; and that the deviations far exceeded any possible 
limits of error of observation. In reply to the question, 
Whether the deviations in question might not be due to the 
action of an unknown planet? he stated that he considered 
it highly probable that such was the case, being systematic, 
and such as might be produced by an exterior planet. I 
then inquired whether he had attempted, from the indica- 
tions afforded by these perturbations, to discover the position 
of the unknown body, in order that 'a hue and cry' might 
be raised for it. From his reply, the words of which I do 
not call to mind, I collected that he had not then gone into 
that inquiry ; but proposed to do so, having now completed 
certain works which had occupied too much of his time. 
And, accordingly, in a letter which I received from him 
after his return to Konigsberg, dated November 14, 1842, 
he says, 'In reference to our conversation at Collingwood, 
I announce to you (melde ich Ihnen) that Uranus is not 
forgotten/ Doubtless, therefore, among his papers will be 
found some researches on the subject. 

"The remarkable calculations of M. Le Verrier which 
have pointed out, as now appears, nearly the true situation 
of the new planet, by resolving the inverse problem of the 
perturbations if uncorroborated by repetition of the numer- 
ical calculations by another hand, or by independent investi- 
gation from another quarter, would hardly justify so strong 
an assurance as that conveyed by my expressions above 
alluded to. But it was known to me, at that time, (I will 
take the liberty to cite the Astronomer Royal as my author- 
ity) that a similar investigation had been independently en- 
tered into, and a conclusion as to the situation of the new 
planet very nearly coincident with M. Le Verrier's arrived 
at (in entire ignorance of his conclusions), by a young 
Cambridge mathematician, Mr. Adams ; 8 who will, I hope, 

* See note 7, page 43. 



386 A BUDGET OF PARADOXES. 

pardon this mention of his name (the matter being one of 
great historical moment), and who will, doubtless, in his 
own good time and manner, place his calculations before the 
public. 

"J. F. W. HERSCHEL." 

Discovery of Le Verrier's Planet. 

Mr. Hind announces to the Times that he has received 
a letter from Dr. Briinnow, of the Royal Observatory at 
Berlin, giving the very important information that Le Ver- 
rier's planet was found by M. Galle, on the night of Sep- 
tember 23. "In announcing this grand discovery," he says, 
"I think it better to copy Dr. Briinnow's 9 letter." 

"Berlin, Sept. 25. 

"My dear Sir. M. Le Verrier's planet was discovered 
here the 23d of September, by M. Galle. 10 It is a star of 
the 8th magnitude, but with a diameter of two or three 
seconds. Here are its places: 

h, m. s. R. A. Declination. 

Sept. 23, 12 14'6 M.T. 328 19' 16'0" 13 24' 8'2" 
Sept. 24. 8 54 40'9 M.T. 328 18' 14'3" 13 24' 29'7' 

The planet is now retrograde, its motion amounting daily 
to four seconds of time. 

"Yours most respectfully, BRUNNOW." 

"This discovery," Mr. Hind says, "may be justly con- 
sidered one of the greatest triumphs of theoretical astron- 
omy;" and he adds, in a postscript, that the planet was ob- 
served at Mr. Bishop's 11 Observatory, in the Regent's Park, 

"Franz Friedrich Ernst Briinnow (1821-1891) was at that time 
or shortly before director of the observatory at Diisseldqrf. He then 
went to Berlin and thence (1854) to Ann Arbor, Michigan. He 
then went to Dublin and finally became Royal Astronomer of Ire- 
land. 

"Johann Gottfried Galle (1812-1910), at that time connected 
with the Berlin observatory, and later professor of astronomy at 
Breslau. 

"George Bishop (1785-1861), in whose observatory in Regent's 
Park important observations were made by Dawes, Hind, and Marth. 



THE NEW PLANET. 387 

on Wednesday night, notwithstanding the moonlight and 
hazy sky. "It appears bright," he says, "and with a power 
of 320 I can see the disc. The following position is the 
result of instrumental comparisons with 33 Aquarii: 
Sept. 30, at 8h. 16m. 21s. Greenwich mean time 

Right ascension of planet 21h. 52m. 47* 15s. 

South declination 13 27' 20"." 

THE NEW PLANET. 

"Cambridge Observatory, Oct. 15. 

"The allusion made by Sir John Herschel, in his letter 
contained in the Athenceum of October 3, to the theoretical 
researches of Mr. Adams, respecting the newly-discovered 
planet, has induced me to request that you would make the 
following communication public. It is right that I should 
first say that I have Mr. Adams's permission to make the 
statements that follow, so far as they relate to his labors. 
I do not propose to enter into a detail of the steps by which 
Mr. Adams was led, by his spontaneous and independent 
researches, to a conclusion that a planet must exist more 
distant than Uranus. The matter is of too great historical 
moment not to receive a more formal record than it would 
be proper to give here. My immediate object is to show, 
while the attention of the scientific public is more particu- 
larly directed to the subject, that, with respect to this re- 
markable discovery, English astronomers may lay claim to 
some merit. 

"Mr. Adams formed the resolution of trying, by calcula- 
tion, to account for the anomalies in the motion of Uranus 
on the hypothesis of a more distant planet, when he was an 
undergraduate in this university, and when his exertions 
for the academical distinction, which he obtained in January 
1843, left him no time for pursuing the research. In the 
course of that year, he arrived at an approximation to the 
position of the supposed planet ; which, however, he did not 
consider to be worthy of confidence, on account of his not 



388 A BUDGET OF PARADOXES. 

having employed a sufficient number of observations of 
Uranus. Accordingly, he requested my intervention to ob- 
tain for him the early Greenwich observations, then in course 
of reduction ; which the Astronomer Royal immediately 
supplied, in the kindest possible manner. This was in Febru- 
ary, 1844. In September, 1845, Mr. Adams communicated 
to me values which he had obtained for the heliocentric 
longitude, excentricity of orbit, longitude of perihelion, and 
mass, of an assumed exterior planet, deduced entirely from 
unaccounted-for perturbations of Uranus. The same re- 
sults, somewhat corrected, he communicated, in October, to 
the Astronomer Royal. M. Le Verrier, in an investigation 
which was published in June of 1846, assigned very nearly 
the same heliocentric longitude for the probable position of 
the planet as Mr. Adams had arrived at, but gave no results 
respecting its mass and the form of its orbit. The coinci- 
dence as to position from two entirely independent investi- 
gations naturally inspired confidence; and the Astronomer 
Royal shortly after suggested the employing of the North- 
umberland telescope of this observatory in a systematic 
search after the hypothetical planet; recommending, at the 
same time, a definite plan of operations. I undertook to 
make the search, and commenced observing on July 29. 
The observations were directed, in the first instance, to the 
part of the heavens which theory had pointed out as the 
most probable place of the planet ; in selecting which I was 
guided by a paper drawn up for me by Mr. Adams. Not 
having hour xxi. of the Berlin star-maps of the publica- 
tion of which I was not aware I had to proceed on the 
principle of comparison of observations made at intervals. 
On July 30, I went over a zone 9' broad, in such a manner 
as to include all stars to the eleventh magnitude. On 
August 4, I took a broader zone and recorded a place of 
the planet. My next observations were on August 12; 
when I met with a star of the eighth magnitude in the zone 
which I had gone over on July 30, and which did not then 



THE NEW PLANET. 389 

contain this star. Of course, this was the planet ; the place 
of which was, thus, recorded a second time in four days 
of observing. A comparison of the observations of July 30 
and August 12 would, according to the principle of search 
which I employed, have shown me the planet. I did not 
make the comparison till after the detection of it at Berlin 
partly because I had an impression that a much more ex- 
tensive search was required to give any probability of dis- 
covery and partly from the press of other occupation. The 
planet, however, was secured, and two positions of it re- 
corded six weeks earlier here than in any other observatory, 
and in a systematic search expressly undertaken for that 
purpose. I give now the positions of the planet on August 
4 and August 12. 



Greenwich mean time. 

"R.A. 21h. 58m. 14 '70s. 



Aug. 4, 13h. 36m. 25s.. . - , Ay p D ^ ^ f ^^ 



j R.A. 
Aug.l2 ) 13h.3m.26s....-{ N J ) JX 



21h. 57m. 26 -13s. 
103 2 r 0'2" 



"From these places compared with recent observations 
Mr. Adams has obtained the following results : 

Distance of the planet from the sun 30*05 

Inclination of the orbit 1 45' 

Longitude of the descending node 309 43' 

Heliocentric longitude, Aug. 4 326 39' 

"The present distance from the sun is, therefore, thirty 
times the earth's mean distance; which is somewhat less 
than the theory had indicated. The other elements of the 
orbit cannot be approximated to till the observations shall 
have been continued for a longer period. 

"The part taken by Mr. Adams in the theoretical search 
after this planet will, perhaps, be considered to justify the 
suggesting of a name. With his consent, I mention Oceanus 
as one which may possibly receive the votes of astronomers. 



390 A BUDGET OF PARADOXES. 

I have authority to state that Mr. Adams's investigations 
will in a short time, be published in detail. 

"J. CHALLIS." 1 

ASTRONOMICAL POLICE REPORT. 

"An ill-looking kind of a body, who declined to give any 
name, was brought before the Academy of Sciences, charged 
with having assaulted a gentleman of the name of Uranus 
in the public highway. The prosecutor was a youngish 
looking person, wrapped up in two or three great coats; 
and looked chillier than anything imaginable, except the 
prisoner, whose teeth absolutely shook, all the time. 

Policeman Le Verrier 1 stated that he saw the prosecutor 
walking along the pavement, and sometimes turning side- 
ways, and sometimes running up to the railings and jerking 
about in a strange way. Calculated that somebody must be 
pulling his coat, or otherwise assaulting him. It was so 
dark that he could not see ; but thought, if he watched the 
direction in which the next odd move was made, he might 
find out something. When the time came, he set Briinnow, 
a constable in another division of the same force, to watch 
where he told him ; and Briinnow caught the prisoner lurk- 
ing about in the very spot, trying to look as if he was 
minding his own business. Had suspected for a long time 
that somebody was lurking about in the neighborhood. 
Briinnow was then called, and deposed to his catching the 
prisoner as described. 

M. Arago. Was the prosecutor sober? 

Le Verrier. Lord, yes, your worship ; no man who had 
a drop in him ever looks so cold as he did. 

M. Arago. Did you see the assault? 

Le Verrier. I can't say I did ; but I told Briinnow 
exactly how he'd be crouched down, just as he was. 

1 James Challis (1803-1882), director of the Cambridge observa- 
tory, and successor of Airy as Plumian professor of astronomy. 

1 On Leverrier and Arago see note 8, page 43, and note 7, page 243. 



ASTRONOMICAL POLICE REPORT. 391 

M. Arago (to Brunnow). Did you see the assault? 

Briinnow. No, your worship ; but I caught the prisoner. 

M. Arago. How did you know there was any assault 
at all? 

Le Verrier. I reckoned it couldn't be otherwise, when 
I saw the prosecutor making those odd turns on the pave- 
ment. 

M . Arago. You. reckon and you calculate ! Why, you'll 
tell me, next, that you policemen may sit at home and find 
out all that's going on in the streets by arithmetic. Did you 
ever bring a case of this kind before me till now? 

Le Verrier. Why, you see, your worship, the police 
are growing cleverer and cleverer every day. We can't 
help it : it grows upon us. 

M. Arago. You're getting too clever for me. What 
does the prosecutor know about the matter? 

The prosecutor said, all he knew was that he was pulled 
behind by somebody several times. On being further ex- 
amined, he said that he had seen the prisoner often, but 
did not know his name, nor how he got his living ; but had 
understood he was called Neptune. He himself had paid 
rates and taxes a good many years now. Had a family of 
six, two of whom got their own living. 

The prisoner being called on for his defence, said that it 
was a quarrel. He had pushed the prosecutor and the 
prosecutor had pushed him. They had known each other 
a long time, and were always quarreling ; he did not know 
why. It was their nature, he supposed. He further said, 
that the prosecutor had given a false account of himself; 
that he went about under different names. Sometimes he 
was called Uranus, sometimes Herschel, and sometimes 
Georgium Sidus ; and he had no character for regularity 
in the neighborhood. Indeed, he was sometimes not to be 
seen for a long time at once. 

The prosecutor, on being asked, admitted, after a little 
hesitation, that he had pushed and pulled the prisoner too. 



392 A BUDGET OF PARADOXES. 

In the altercation which followed, it was found very diffi- 
cult to make out which began : and the worthy magistrate 
seemed to think they must have begun together. 

M. Arago. Prisoner, have you any family? 

The prisoner declined answering that question at present. 
He said he thought the police might as well reckon it out 
whether he had or not. 

M. Arago said he didn't much differ from that opinion. 
He then addressed both prosecutor and prisoner ; and told 
them that if they couldn't settle their differences without 
quarreling in the streets, he should certainly commit them 
both next time. In the meantime, he called upon both to 
enter into their own recognizances ; and directed the police 
to have an eye upon both, observing that the prisoner 
would be likely to want it a long time, and the prosecutor 
would be not a hair the worse for it." 

This quib was written by a person who was among the 
astronomers : and it illustrates the fact that Le Verrier had 
sole possession of the field until Mr. Challis's letter appeared. 
Sir John Herschel's pervious communication should have 
paved the way: but the wonder of the discovery drove it 
out of many heads. There is an excellent account of the 
whole matter in Professor Grant's 2 History of Physical 
Astronomy. The squib scandalized some grave people, who 
wrote severe admonitions to the editor. There are formalists 
who spend much time in writing propriety to journals, to 
which they serve as foolometers. In a letter to the Athe- 
nceum, speaking of the way in which people hawk fine terms 
for common things, I said that these people ought to have 
a new translation of the Bible, which should contain the 
verse "gentleman and lady, created He them." The editor 
was handsomely fired and brimstoned ! 

'Robert Grant's (1814-1892) History of Physical Astronomy 
from the ^Earliest Ages to the Middle of the Nineteenth Century 
appeared in 1852. He was professor of astronomy and director of 
the observatory at Glasgow. 



A NEW THEORY OF TIDES. 393 



A NEW THEORY OF TIDES. 

A new theory of the tides: in which the errors of the usual 
theory are demonstrated; and proof shewn that the full moon 
is not the cause of a concomitant spring tide, but actually the 
cause of the neaps.... By Comm r . Debenham, 1 R.N. London, 
1846, 8vo. 

The author replied to a criticism in the Athenaum, and 
I remember how, in a very few words, he showed that he 
had read nothing on the subject. The reviewer spoke of 
the forces of the planets (i. e., the Sun and Moon) on the 
ocean, on which the author remarks, "But N.B. the Sun is 
no planet, Mr. Critic." Had he read any of the actual in- 
vestigations on the usual theory, he would have known that 
to this day the sun and moon continue to be called planets 
though the phrase is disappearing in speaking of the tides ; 
the sense, of course, being the old one, wandering bodies. 

A large class of the paradoxers, when they meet with 
something which taken in their sense is absurd, do not take 
the trouble to find out the intended meaning, but walk off 
with the words laden with their own first construction. Such 
men are hardly fit to walk the streets without an interpreter. 
I was startled for a moment, at the time when a recent happy 
and more recently happier marriage occupied the public 
thoughts, by seeing in a haberdasher's window, in staring 
large letters, an unpunctuated sentence which read itself to 
me as "Princess Alexandra! collar and cuff!" It imme- 
diately occurred to me that had I been any one of some 
scores of my paradoxers, I should, no doubt, have proceeded 
to raise the mob against the unscrupulous person who dared 
to hint to a young bride such maleficent or at least immel- 
lificent conduct towards her new lord. But, as it was, cer- 
tain material contexts in the shop window suggested a less 

1 John Debenham was more interested in religion than in astron- 
omy. He wrote The Strait Gate; or, the true scripture doctrine of 
salvation clearly explained, London, 1843, and Tractatus de magis et 
Bethlehema stella et Christi in deserto tentatione, privately printed 
at London in 1845. 



394 A BUDGET OF PARADOXES. 

savage explanation. A paradoxer should not stop at reading 
the advertisements of Newton or Laplace : he should learn to 
look at the stock of goods. 

I think I must have an eye for double readings, when 
presented : though I never guess riddles. On the day on 
which I first walked into the Panizzi reading room 2 as it 
ought to be called at the Museum, I began my circuit of 
the wall-shelves at the ladies' end : and perfectly coincided in 
the propriety of the Bibles and theological works being 
placed there. But the very first book I looked on the back 
of had, in flaming gold letters, the following inscription 
"Blast the Antinomians !" 3 If a line had been drawn below 
the first word, Dr. Blast's history of the Antinomians would 
not have been so fearfully misinterpreted. It seems that 
neither the binder nor the arranger of the room had caught 
my reading. The book was removed before the catalogue 
of books of reference was printed. 

AN ASTRONOMICAL PARADOXER. 

Two systems of astronomy : first, the Newtonian system, showing 
the rise and progress thereof, with a short historical account ; the 
general theory with a variety of remarks thereon : second, the 
system in accordance with the Holy Scriptures, showing the 
rise and progress from Enoch, the seventh from Adam, the 
prophets, Moses, and others, in the first Testament; our Lord 
Jesus Christ, and his apostles, in the new or second Testament ; 
Reeve and Muggleton, in the third and last Testament; with 
a variety of remarks thereon. By Isaac Frost. 1 London, 1846, 
4to. 

"More properly the Sydney Smirke reading room, since it was 
built from his designs. 

* The Antinomians were followers of Johannes Agricola (1494- 
1566). They believed that Christians as such were released from all 
obligations to the Old Testament. Some went so far as to assert 
that, since all Christians were sanctified, they could not lose this 
sanctity even though they disobeyed God. The sect was prominent 
in England in the seventeenth century, and was transferred to New 
England. Here it suffered a check in the condemnation of Mrs. Ann 
Hutchinson (1636) by the Newton Synod. 

1 Aside from this work and his publications on Reeve and 
Muggleton he wrote nothing. With Joseph Frost he published A list 



AN ASTRONOMICAL PARADOXER. 395 

A very handsomely printed volume, with beautiful plates. 
Many readers who have heard of Muggletonians have never 
had any distinct idea of Lodowick Muggleton, 2 the inspired 
tailor, (1608-1698) who about 1650 received his commission 
from heaven, wrote a Testament, founded a sect, and de- 
scended to posterity. Of Reeve 3 less is usually said ; accord- 
ing to Mr. Frost, he and Muggleton are the two "witnesses." 
I shall content myself with one specimen of Mr. Frost's 
science : 

"I was once invited to hear read over 'Guthrie 4 on As- 
tronomy,' and when the reading was concluded I was asked 
my opinion thereon ; when I said, 'Doctor, it appears to me 
that Sir I. Newton has only given two proofs in support of 
his theory of the earth revolving round the sun : all the rest 
is assertion without any proofs.' 'What are they?' inquired 
the Doctor. 'Well/ I said, 'they are, first, the power of 

of Books and general index to J. Reeve and L. Muggleton's works 
(1846), Divine Songs of the Muggletonians (1829), and the work 
mentioned on page 396. The works of J. Reeve and L. Muggleton 
(1832). 

'About 1650 he and his cousin John Reeve (1608-1658) began 
to have visions. As part of their creed they taught that astronomy 
was opposed by the Bible. They asserted that the sun moves about 
the earth, and Reeve figured out that heaven was exactly six miles 
away. Both Muggleton and Reeve were imprisoned for their uni- 
tarian views. Muggleton wrote a Transcendant Spirituall Treatise 
(1652). I have before me A true Interpretation of All the Chief 

Texts of the whole Book of the Revelation of St. 'John By 

Lodozvick Muggleton, one of the two last Commissioned Witnesses 
& Prophets of the onely high, immortal, glorious God, Christ Jesus 
(1665), in which the interpretation of the "number of the beast" 
occupies four pages without arriving anywhere. 

*In 1652 he was, in a vision, named as the Lord's "last mes- 
senger," with Muggleton as his "mouth," and died six years later, 
probably of nervous tension resulting from his divine "illumination." 
He was the more spiritual of the two. 

4 William Guthrie (1708-1770) was a historian and political 
writer. His History of England (1744-1751) was the first attempt 
to base history on parliamentary records. He also wrote a General 
History of Scotland in 10 volumes (1767). The work to which Frost 
refers is the Geographical, Historical, and Commercial Grammar 
(1770) which contained an astronomical part by J. Ferguson. By 
1827 it had passed through 24 editions. 



396 A BUDGET OF PARADOXES. 

attraction to keep the earth to the sun ; the second is the 
power of repulsion, by virtue of the centrifugal motion of 
the earth: all the rest appears to me assertion without 
proof.' The Doctor considered a short time and then said, 
'It certainly did appear so.' I said, 'Sir Isaac has certainly 
obtained the credit of completing the system, but really he 
has only half done his work.' 'How is that/ inquired my 
friend the Doctor. My reply was this: 'You will observe 
his system shows the earth traverses round the sun on an 
inclined plane; the consequence is, there are four powers 
required to make his system complete: 

1st. The power of attraction. 

2ndly. The power of repulsion. 

3rdly. The power of ascending the inclined plane. 

4thly. The power of descending the inclined plane 

You will thus easily see the four powers required, and 
Newton has only accounted for two ; the work is therefore 
only half done/ Upon due reflection the Doctor said, 'It 
certainly was necessary to have these four points cleared 
up before the system could be said to be complete.' " 

I have no doubt that Mr. Frost, and many others on 
my list, have really encountered doctors who could be 
puzzled by such stuff as this, or nearly as bad, among the 
votaries of existing systems, and have been encouraged 
thereby to print their objections. But justice requires me 
to say that from the words "power of repulsion by virtue 
of the centrifugal motion of the earth," Mr. Frost may be 
suspected of having something more like a notion of the 
much-mistaken term "centrifugal force" than many para- 
doxers of greater fame. The Muggletonian sect is not alto- 
gether friendless: over and above this handsome volume, 
the works of Reeve and Muggleton were printed, in 1832, 
in three quarto volumes. See Notes and Queries, ist Series, 
v, 80 ; 3d Series, iii, 303. 



AN ASTRONOMICAL PARADOXER. 397 

[The system laid down by Mr. Frost, though intended 
to be substantially that of Lodowick Muggleton, is not so 
vagarious. It is worthy of note how very different have 
been the fates of two contemporary paradoxers, Muggleton 
and George Fox. 5 They were friends and associates, 6 and 
commenced their careers about the same time, 1647-1650. 
The followers of Fox have made their sect an institution, 
and deserve to be called the pioneers of philanthropy. But 
though there must still be Muggletonians, since expensive 
books are published by men who take the name, no sect of 
that name is known to the world. Nevertheless, Fox and 
Muggleton are men of one type, developed by the same 
circumstances : it is for those who investigate such men to 
point out why their teachings have had fates so different. 
Macaulay says it was because Fox found followers of more 
sense than himself. True enough: but why did Fox find 
such followers and not Muggleton? The two were equally 
crazy, to all appearance: and the difference required must 
be sought in the doctrines themselves. 

Fox was not a rational man : but the success of his sect 
and doctrines entitles him to a letter of alteration of the 
phrase which I am surprised has not become current. When 
Conduitt, 7 the husband of Newton's half-niece, wrote a 
circular to Newton's friends, just after his death, inviting 
them to bear their parts in a proper biography, he said, "As 
Sir I. Newton was a national man, I think every one ought 
to contribute to a work intended to do him justice." Here 
is the very phrase which is often wanted to signify that 



G George Fox (1624-1691), founder of the Society of Friends; a 
mystic and a disciple of Boehme. He was eight times imprisoned for 
heresy. 

6 If they were friends they were literary antagonists, for Mug- 
gleton wrote against Fox The Neck of the Quakers Broken (1663), 
and Fox replied in 1667. Muggleton also wrote A Looking Glass for 
George Fox. 

'John Conduitt (1688-1737), who married (1717) Newton's 
half niece, Mrs. Katherine Barton. See note 6, page 136. 



398 A BUDGET OF PARADOXES. 

celebrity which puts its mark, good or bad, on the national 
history, in a manner which cannot be asserted of many 
notorious or famous historical characters. Thus George 
Fox and Newton are both national men. Dr. Roget's 8 
Thesaurus gives more than fifty synonyms colleagues 
would be the better word of "celebrated" any one of 
which might be applied, either in prose or poetry, to New- 
ton or to his works, no one of which comes near to the 
meaning which Conduitt's adjective immediately suggests. 
The truth is, that we are too monarchical to be national. 
We have the Queen's army, the Queen's navy, the Queen's 
highway, the Queen's English, etc. ; nothing is national ex- 
cept the debt. That this remark is not new is an addition 
to its force; it has hardly been repeated since it was first 
made. It is some excuse that nation is not vernacular Eng- 
lish: the country is our word, and country man is appro- 
priated.] 



Astronomical Aphorisms, or Theory of Nature ; founded on the 
immutable basis of Meteoric Action. By P. Murphy, 9 Esq. 
London, 1847, 12mo. 

This is by the framer of the Weather Almanac, who 
appeals to that work as corroborative of his theory of plan- 
etary temperature, years after all the world knew by ex- 
perience that this meteorological theory was just as good 
as the others. 



"Probably Peter Mark Roget's (1779-1869) Thesaurus of Eng- 
lish Words (1852) is not much used at present, but it went through 
28 editions in his lifetime. Few who use the valuable work are 
aware that Roget was a professor of physiology at the Royal Insti- 
tution (London), that he achieved his title of F. R. S. because of his 
work in perfecting the slide rule, and that he followed Sir John 
Herschel as secretary of the Royal Society. 

* See note 1, page 327. This work went into a second edition in 
the year of its first publication. 



THEISM INDEPENDENT OF REVELATION. 399 

The conspiracy of the Bullionists as it affects the present system 
of the money laws. By Caleb Quotem. Birmingham, 1847, 
8vo. (pp. 16). 

This pamphlet is one of a class of which I know very 
little, in which the effects of the laws relating to this or 
that political bone of contention are imputed to deliberate 
conspiracy of one class to rob another of what the one knew 
ought to belong to the other. The success of such writers 
in believing what they have a bias to believe, would, if they 
knew themselves, make them think it equally likely that the 
inculpated classes might really believe what it is their in- 
terest to believe. The idea of a guilty understanding ex- 
isting among fundholders, or landholders, or any holders, 
all the country over, and never detected except by bouncing 
pamphleteers, is a theory which should have been left for 
Cobbett 10 to propose, and for Apella to believe. 11 

[August, 1866. A pamphlet shows how to pay the 
National Debt. Advance paper to railways, etc., receivable 
in payment of taxes. The railways pay interest and prin- 
cipal in money, with which you pay your national debt, and 
redeem your notes. Twenty-five years of interest redeems 
the notes, and then the principal pays the debt. Notes to 
be kept up to value by penalties.] 



THEISM INDEPENDENT OF REVELATION. 

The Reasoner. No. 45. Edited by G. J. Holyoake. 1 Price 2d. 
Is there sufficient proof of the existence of God? 8vo. 1847. 

This acorn of the holy oak was forwarded to me with 
a manuscript note, signed by the editor, on the part of the 

10 See note 1, page 177. 

11 See note 4, page 233. 

1 George Jacob Holyoake (1817-1906) entered into a controver- 
sial life at an early age. In 1841 he was imprisoned for six months 
for blasphemy. He founded and edited The Reasoner (Vols. 1-26, 
1846-1861). In his later life he did much to promote cooperation 
among the working class. 



400 A BUDGET OF PARADOXES. 

"London Society of Theological Utilitarians," who say, 
"they trust you may be induced to give this momentous 
subject your consideration." The supposition that a middle- 
aged person, known as a student of thought on more subjects 
than one, had that particular subject yet to begin, is a speci- 
men of what I will call the assumption-trick of controversy, 
a habit which pervades all sides of all subjects. The tract is 
a proof of the good policy of letting opinions find their 
level, without any assistance from the Court of Queen's 
Bench. Twenty years earlier the thesis would have been 
positive, "There is sufficient proof of the non-existence of 
God," and bitter in its tone. As it stands, we have a mod- 
erate and respectful treatment wrong only in making the 
opponent argue absurdly, as usually happens when one 
side invents the other of a question in which a great many 
Christians have agreed with the atheist: that question be- 
ing Can the existence of God be proved independently of 
revelation? Many very religious persons answer this ques- 
tion in the negative, as well as Mr. Holyoake. And, this 
point being settled, all who agree in the negative separate 
into those who can endure scepticism, and those who can- 
not: the second class find their way to Christianity. This 
very number of The Reasoner announces the secession of 
one of its correspondents, and his adoption of the Christian 
faith. This would not have happened twenty years before : 
nor, had it happened, would it have been respectfully an- 
nounced. 

There are people who are very unfortunate in the ex- 
pression of their meaning. Mr. Holyoake, in the name of 
the "London Society" etc., forwarded a pamphlet on the 
existence of God, and said that the Society trusted I "may 
be induced to give" the subject my "consideration." How 
could I know the Society was one person, who supposed 
I had arrived at a conclusion and wanted a "guiding word" ? 
But so it seems it was: Mr. Holyoake, in the English 



THEISM INDEPENDENT OF REVELATION. 401 

Leader of October 15, 1864, and in a private letter to me, 
writes as follows : 

"The gentleman who was the author of the argument, 
and who asked me to send it to Mr. De Morgan, never 
assumed that that gentleman had 'that particular subject 
to begin' on the contrary, he supposed that one whom we 
all knew to be eminent as a thinker had come to a conclusion 
upon it, and would perhaps vouchsafe a guiding word to 
one who was, as yet, seeking the solution of the Great Prob- 
lem of Theology. I told my friend that 'Mr. De Morgan 
was doubtless preoccupied, and that he must be content to 
wait. On some day of courtesy and leisure he might have 
the kindness to write/ Nor was I wrong the answer ap- 
pears in your pages at the lapse of seventeen years." 

I suppose Mr. Holyoake's way of putting his request 
was the stylus curio? of the Society. A worthy Quaker 
who was sued for debt in the King's Bench was horrified 
to find himself charged in the declaration with detaining 
his creditor's money by force and arms, contrary to the peace 
of our Lord the King, etc. It's only the stylus curioe, said 
a friend: I don't know curio? , said the Quaker, but he 
shouldn't style us peace-breakers. 

The notion that the won-existence of God can be proved, 
has died out under the light of discussion: had the only 
lights shone from the pulpit and the prison, so great a 
step would never have been made. The question now is 
as above. The dictum that Christianity is "part and parcel 
of the law of the land" is also abrogated : at the same time, 
and the coincidence is not an accident, it is becoming some- 
what nearer the truth that the law of the land is part and 
parcel of Christianity. It must also be noticed that Chris- 
tianity was part and parcel of the articles of war] and so 
was duelling. Any officer speaking against religion was to 
be cashiered ; and any officer receiving an affront without, 
in the last resort, attempting to kill his opponent, was also 
to be cashiered. Though somewhat of a book-hunter, I 



402 A BUDGET OF PARADOXES. 

have never been able to ascertain, the date of the collected 
remonstrances of the prelates in the House of Lords against 
this overt inculcation of murder, under the soft name of 
satisfaction: it is neither in Watt, 2 nor in Lowndes, 3 nor in 
any edition of Brunet ;* and there is no copy in the British 
Museum. Was the collected edition really published? 

[The publication of the above in the Athenceum has not 
produced reference to a single copy. The collected edition 
seems to be doubted. I have even met one or two persons 
who doubt the fact of the Bishops having remonstrated at 
all: but their doubt was founded on an absurd supposition, 
namely, that it was no business of theirs ; that it was not the 
business of the prelates of the church in union with the 
state to remonstrate against the Crown commanding mur- 
der! Some say that the edition was published, but under 
an irrelevant title, which prevented people from knowing 
what it was about. Such things have happened: for ex- 
ample, arranged extracts from Wellington's general orders, 
which would have attracted attention, fell dead under the 
title of "Principles of War." It is surmised that the book 
I am looking for also contains the protests of the Reverend 
bench against other things besides the Thou-shalt-do-murder 
of the Articles (of war), and is called "First Elements of 
Religion" or some similar title. Time clears up all things.] 

8 See note 6, page 102. 

'William Thomas Lowndes (1798-1843), whose Bibliographer's 
Manual of English Literature, 4 vols., London, 1834 (also 1857-1864, 
and 1869) is a classic in its line. 

4 Jacques Charles Brunet (1780-1867), the author of the great 
French bibliography, the Manuel du Libraire (1810). 



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